Association between population distribution and urban GDP scaling
Haroldo V. Ribeiro, Milena Oehlers, Ana I. Moreno-Monroy, Jurgen P. Kropp, Diego Rybski
AAssociation between population distribution and urban GDPscaling
Haroldo V. Ribeiro , Milena Oehlers , Ana I. Moreno-Monroy , J¨urgen P. Kropp ,Diego Rybski † , Departamento de F´ısica, Universidade Estadual de Maring´a – Maring´a, PR 87020-900,Brazil Potsdam Institute for Climate Impact Research – PIK, Member of LeibnizAssociation, P.O. Box 601203, 14412 Potsdam, Germany OECD, 1 Rue Andr´e Pascal, 75016, Paris, France; Department of Geography andPlanning, University of Liverpool, Chatham St, Liverpool L69 7ZT, United Kingdom Institute for Environmental Science and Geography, University of Potsdam, 14476Potsdam, Germany Department of Environmental Science Policy and Management, University ofCalifornia Berkeley, 130 Mulford Hall † [email protected] Abstract
Urban scaling and Zipf’s law are two fundamental paradigms for the science of cities.These laws have mostly been investigated independently and are often perceived asdisassociated matters. Here we present a large scale investigation about the connectionbetween these two laws using population and GDP data from almost five thousandconsistently-defined cities in 96 countries. We empirically demonstrate that both lawsare tied to each other and derive an expression relating the urban scaling and Zipfexponents. This expression captures the average tendency of the empirical relationbetween both exponents, and simulations yield very similar results to the real data afteraccounting for random variations. We find that while the vast majority of countriesexhibit increasing returns to scale of urban GDP, this effect is less pronounced incountries with fewer small cities and more metropolises (small Zipf exponent) than incountries with a more uneven number of small and large cities (large Zipf exponent).Our research puts forward the idea that urban scaling does not solely emerge fromintra-city processes, as population distribution and scaling of urban GDP are correlatedto each other.
Introduction
Physical measurements such as weight or size of objects are always confined to specificscales. However, the outcomes of several natural phenomena and socio-economicprocesses can extend across multiple orders of magnitude [1]. Examples of such systemsare as diverse as earthquakes [2], stock market fluctuations [3], casualties in humaninsurgencies [4], and fracture of materials [5]. These systems usually share non-trivialstatistical regularities manifested in the form of power-law distributions or power-lawrelations, the so-called scaling laws. Cities are among these systems as they occur insizes from thousands to tens of million inhabitants. Urban systems are also well knownJanuary 11, 2021 1/17 a r X i v : . [ phy s i c s . s o c - ph ] J a n o follow scaling relations in time and space, as summarized by Batty [6] in the “sevenlaws of urban scaling”.Zipf’s law [7, 8] and Bettencourt-West law [9] are two of the best-known scaling lawsemerging in urban systems. Initially observed by Auerbach [8] and then popularized byZipf [7], Zipf’s law for cities states that the distribution of city populations, for a givenregion or country, is approximated by an inverse power-law function (or the rank-sizerule), implying that there are plenty of small cities and very few metropolises.Bettencourt-West law [9], better known as “urban scaling”, establishes a power-lawrelation between urban indicators and city population. Urban scaling is well illustratedby the concept of agglomeration economies in cities [10, 11], in which the power-lawassociation between urban wealth and population implies that urban wealth increasesmore than proportionally with city population.Fostered by a recent deluge of highly-detailed city data, researchers from diversedisciplines such as geography, economics, or physics have devoted ongoing efforts inidentifying and understanding fundamental principles and regularities underlying urbansystems [1, 6, 12–14]. While most of these works are either concerned with Zipf’slaw [15–25] or urban scaling [26–34], very few have tackled the relationship betweenboth. Zipf’s law and urban scaling have mostly been studied independently because it iscommonly assumed that both laws are independent descriptions of urban systems acrosscountries. The few investigations on possible connections between Zipf’s law and urbanscaling have a more local character and explore this association within countries [35, 36].The work of Gomez-Lievano et al. [35] is seminal in this regard and has shown that(under certain conditions) urban scaling can be related to Zipf’s law when urbanindicators are also power-law distributed. This connection is obtained from probabilitydistributions and shows that the urban scaling exponent has an upper limit determinedby both the Zipf exponent and the power-law exponent that characterizes the urbanindicator distribution. This result however does not imply that these three exponentsare directly associated with each other. In fact, random permutations of population andurban indicator values only have the effect of removing a possible correlation betweenthe two variables, but do not have the effect of changing their distribution.To date, there has been no attempt to empirically investigate the associationbetween urban scaling and Zipf’s law across a large number of countries. The paucity ofsuch studies certainly reflects the lack of consistent and comparable data acrosscountries. A convincing comparison between these two laws demands a unified citydefinition across the globe as well as measures of population and urban indicators basedon this same definition. And it was not until very recently that satisfying thisrequirement has become possible. Here we use a new harmonized city definition forinvestigating Zipf’s law and urban scaling over almost five thousand cities in 96countries. By analyzing population and gross domestic product (GDP) of these citiesper country, we estimate the Zipf and the urban scaling exponents to probe for apossible relation between these two scaling laws. Our empirical results show that bothexponents are indeed related to each other and that a functional form of this associationcan be exactly derived from scaling relations emerging at the country level.We demonstrate that Zipf’s law and urban scaling imply a power-law relationbetween total urban population and total urban GDP of countries, where the countryscaling exponent is dependent on the Zipf and the urban scaling exponents. Becausecountry-aggregated values of urban population and GDP are fixed, there is only onecountry scaling exponent for total GDP, which in turn associates the urban scalingexponent to the Zipf exponent. We verify the integrity of our model by estimating thecountry-scaling exponents from the empirical relationship between the Zipf and theurban scaling exponents, and also by showing that numerical simulations yield resultsvery similar to those obtained from real-world data. The connection between bothJanuary 11, 2021 2/17xponents shows that urban scaling does not only emerge from processes occurringwithin the city boundaries; instead, it suggests that the population distribution of anurban system does affect urban scaling or vice versa. For the particular case of urbanGDP, while almost all countries exhibit increasing returns to scale (urban scalingexponent greater than one), our findings indicate this effect is smaller in countries witha more balanced number of small and large cities (small Zipf exponent) than in countrieswith a more unbalanced number of small and large cities (large Zipf exponent). Results
Empirical connection between both scaling laws
We start by revisiting Zipf’s law and the urban scaling law. Zipf’s law for cities [7]establishes that the rank r and the city population s of an urban system are relatedthrough a power-law function r ∼ s − α , (1)where α > α varies across countries and epochs,but α ≈ y and the citypopulation s within an urban system, that is, y = c s β , (2)where c > β is the urban scaling exponent. The value of β dependson the type of urban indicator, but increasing returns to scale ( β >
1) are usuallyreported for socio-economic indicators, decreasing returns to scale ( β <
1) forinfrastructure indicators, and constant returns to scale ( β = 1) for indicators related toindividual needs [9]. The values of α and β are also susceptible to different citydefinitions [23, 37], and we thus need a unified definition across different urban systemsto test a possible association between their values.To do so, we use a generalized definition of functional urban areas (FUA) recentlyproposed by Moreno-Monroy et al. [38, 39]. The concept of FUA was initially developedfor countries of the OECD and Europe as a unified definition of metropolitan areas,consisting of high-density urban cores and their surrounding areas of influence orcommuting areas. The generalized definition we use (so-called eFUA or GHSL-FUA)represents an extension of this concept to countries of the entire globe. By consideringthe areas of influence of urban cores, eFUAs give a less fragmented representation of thecity size distribution because dense clusters proximate to urban cores are rightly notconsidered as independent cities. While eFUAs delineate world-wide comparable cityboundaries, the majority of urban indicators are available at the level of localadministrative units, that in addition to not being centralized into a global data set,may change from country to country. We avoid this problem by considering a globalgridded data set for GDP [40] (see Materials and Methods). Thus, by combining thesetwo data sources (see Materials and Methods and Fig. 1 in S1 Appendix), we create aconsistent data set comprising the population ( s ) and the GDP ( y ) of 4,571 cities from96 countries.Having this harmonized data set, we estimate the Zipf exponent α and urban scalingexponent β after grouping the values of s and y by country (see Materials and Methods).The scatter plot in Fig. 1A depicts the values of β versus α , where the insets showZipf’s law and urban scaling of city GDP for three countries. As these three examplesillustrate, the data follows Zipf’s law and urban scaling with deviations comparable withother studies about these two laws (see S1 Appendix, Sec. 4 for all countries). TheJanuary 11, 2021 3/17 .5 1.0 1.5 2.0 2.5 3.0 Zipf exponent, U r ban sc a li ng e x ponen t, = ± = ± = ± = 1=1.22 City population, log s C i t y r an k , l o g r City population, log s C i t y G D P , l o g y Turkey = ± = ± City population, log s C i t y r an k , l o g r City population, log s C i t y G D P , l o g y Russia = ± = ± City population, log s C i t y r an k , l o g r City population, log s C i t y G D P , l o g y Australia = ± = ± Urban scaling exponent,
Zipf exponent,
A BC
Fig 1.
Association between the urban scaling exponent β and the Zipf exponent α . (A) Values of β versus α for each countryin our data set. The three different markers distinguish countries according to the tercile values of the total urban GDPdistribution (for instance, high-GDP countries have highest ≈
33% GDP values). The horizontal dashed line shows the β = 1while the inclined dashed line represents the β = α relationship. As we shall discuss in the next section, the continuous lineshows the model of Eq. (9) adjusted to data and the gray shaded region stands for the 95% confidence band. The coloredbackground represents the different intervals of α defined in Eq. (9). The insets (indicated by blue arrows) illustrate Zipf’s lawfor city population (left) and the urban scaling relationship of city GDP (right) for three countries (see S1 Appendix, Sec. 4for all considered countries). We have verified that the model of Eq. (9) provides a significantly better description of datawhen compared with a null model where β is independent of α (intercept-only model: β = constant, see Fig. 4 in S1Appendix), and that statistical correlations between β and α are significantly enhanced in the (orange shaded) region whereour model predicts a linear correspondence between the exponents (Fig. 5 in S1 Appendix). Maps in panels (B) and (C) showthe color-coded values of α and β for each country (light gray indicates missing values).world maps in Figs. 1B and C indicate the regional distribution of the values of α and β .In line with the meta-analysis of Refs. [18, 23], we find Zipf exponents α roughlydistributed around 1 with average value and standard deviation equal to 1 .
24 and 0 . ≈
94% of the countries exhibit urbanscaling exponents with GDP ( β ) larger than 1 (Fig. 2B in S1 Appendix), and theaverage value and standard deviation of β are 1 .
16 and 0 .
17, respectively. This resultagrees with the idea that economic indicators display increasing returns to scale [9, 41].The results shown in Fig. 1 suggest a positive association between the values of β and α , that is, an increase of the Zipf exponent α appears to come along with a rise inthe urban scaling exponent β (or vice versa). This behavior is also perceptible in theworld maps, where we note that regional differences in the values of α (Fig. 1B) aresimilar to the ones observed for β (Fig. 1C). However, these visual similarities aremainly induced by the largest countries in land area, and a more careful analysis ofthese maps reveals important differences, especially in the African continent andJanuary 11, 2021 4/17entral Asia. These differences are more evident in the scatter plot of Fig. 1A, wherewe observe a considerable spread in the association between both exponents. We havefurther quantified the association between the values of β and α by estimating theSpearman rank correlation and the Pearson correlation within a sliding window of size∆ α (cid:48) centered in α (cid:48) . For different values of ∆ α (cid:48) , we find that the correlations peakaround α (cid:48) ≈ . α (cid:48) (Fig. 3 in S1 Appendix). This analysisthus suggests that the overall association between both exponents is non-linear and that β may approach constant values for large and small values of α . Country scaling and the association between both exponents
To better describe the empirical connection between the urban scaling exponent and theZipf exponent, we hypothesize that this association can be derived from the relationshipbetween country-aggregated values of urban population ( S ) and urban GDP ( Y ). As weshall show, the combination of Zipf’s and the urban scaling laws implies a power-lawrelation between total urban population S and total urban GDP Y . This countryscaling law is characterized by an exponent γ that is a function of β and α , which inturn yields a mathematical expression for the relation between β and α . To do so, westart by noticing that Zipf’s law implies a power-law dependence for the absolutenumber of cities with population s , that is, p ( s ) = ks − ( α +1) for s min < s < s max , where s min and s max represent a lower and an upper cutoff associated to the smallest andlargest city population of a particular urban system, and k is a normalization constant(see S1 Appendix, Sec. 1 for details). By combining this frequency function p ( s ) withurban scaling (Eq. 2), we can write the total urban GDP of a country as Y = s max (cid:88) s = s min cs β p ( s ) ≈ kc (cid:90) s max s min s β − α − ds , (3)where the normalization constant k is determined by S = s max (cid:88) s = s min sp ( s ) ≈ k (cid:90) s max s min s − α ds . (4)To solve these equations, we consider that s min and s max are power-law functions of Ss min = aS δ , (5) s max = bS θ , (6)where a > b > δ > θ > Y = c ( α − Sα − β (cid:18) a β b α S δβ + θα − a α b β S θβ + δα ab α S δ + θα − a α bS θ + δα (cid:19) , (7)that in the limit of S (cid:29) Y = Y S γ , (8)where Y is a constant and γ = γ ( α, β, δ, θ ) is the country scaling exponent for totalurban GDP. As detailed in S1 Appendix, Sec. 1, the exact form of γ depends onconditions imposed on the exponents α , β , δ , and θ (cases A.1-A.8 in S1 Appendix)which in turn emerge from determining the dominant term of Eq. (7) in the limit of S (cid:29)
1. Therefore, the combination of Zipf’s law (Eq. 1) with the urban scaling (Eq. 2)January 11, 2021 5/17nd the country scaling relations of s min and s max (Eqs. 5 and 6) leads us to the countryscaling of total urban GDP (Eq. 8), where the exponent γ depends on α , β , δ and θ .The country scaling relations of GDP and s max have previously been empiricallyobserved in Refs. [42–44]. We have also verified that Eqs. (8), (5), and (6) hold well forthe country-aggregated values in our data set with γ > δ < θ (Fig. 6 in S1Appendix). More importantly, while α and β are intra-country exponents havingdifferent values for each country, γ , δ and θ are inter-country exponents and there isonly one value for each across all countries. Thus, we can solve γ = γ ( α, β, δ, θ ) for β (S1 Appendix, Sec. 1 for details) to find β = γ − θ < α ≤ γ + δ − θ + (cid:0) − δθ (cid:1) α < α < γ − δ γ − δ α ≥ γ − δ , (9)for γ > δ < θ . This piecewise relationship implies that β is a constant up to α = 1, where it starts to increase linearly until reaching the diagonal line given by β = α , and then continues as another constant. It is worth mentioning that by writing β as a function of α , we are not assuming any causal direction for the associationbetween both exponents. Indeed, we could also solve γ = γ ( α, β, δ, θ ) for α but thisyields a non-functional dependency, that is, the horizontal plateaus defined by Eq. (9)become vertical lines when writing α as function of β .We have adjusted Eq. (9) to the empirical relation between α and β (see Materialsand Methods) and the best fitting parameters are γ = 1 . ± . δ = 0 . ± .
05, and θ = 0 . ± .
03. The solid line in Fig. 1A represents the best fit of Eq. (9) and thecolored background indicates the different ranges of α defined in Eq. (9). Despite thelarge variations in the data, our model captures the average tendency of the empiricalrelation between β and α . We have verified that the statistical correlations between thevalues of β and α are only statistically significant in the mid-range of α values, whilethere are no significant correlations within the lower and higher ranges of α values(Fig. 5 in S1 Appendix). Furthermore, the Akaike and Bayesian information criteriaindicate that it is at least 100 times more likely that the empirical data come from ourmodel (Eq. 9) than from a null-model assuming no relationship between both exponents(intercept-only model: β = constant, see Fig. 4 in S1 Appendix). We also find that theestimated parameters from Eq. (9) are quite robust against thresholds for the totalGDP; the adjusted values of γ , δ , and δ barely change, even if we only consider thecountries with top 50% GDP values (Fig. 7 in S1 Appendix).In addition to the previous model validation, the adjustment of Eq. (9) allows us toverify the consistency of our modeling approach through the country scalingrelationships. Specifically, the country scaling exponents estimated from Eq. (9) shoulddescribe well the empirical country scaling relationships. To do so, we have adjusted thecountry scaling relationships of Eqs. (5), (6), and (8) by considering only the prefactors( a , b , and Y ) as fitting parameters and fixing country scaling exponents ( δ , θ and γ ) tothe values estimated from Eq. (9). Figures 2A-C show that the three country scalingrelations describe quite well the empirical data. Furthermore, the country scalingexponents obtained by fitting Eq. (9) to the empirical relationship between β and α agree well with the estimates directly obtained from the country scaling relations, thatis, by fitting Eqs. (5), (6), and (8) to the country-aggregated data, as shown in Fig. 2D.The values of δ and θ estimated from both approaches are not significantly different,while the values of γ are both above one but fitting the country scaling directly fromdata yields a slightly larger value. We believe this result provides support for our model,especially when considering the level of observed variation in the relationship between β and α as well as that in the country scaling relations.January 11, 2021 6/17 .5 7.0 7.5 8.0 8.5 Country's urban population, log S U r ban G D P , l o g Y Pearson's R = 0.78 A = log Y = ± Country's urban population, log S S m a ll e s t c i t y popu l a t i on , l o g s m i n Pearson's R = 0.40 B = log a = ± Country's urban population, log S La r ge s t c i t y popu l a t i on , l o g s m a x Pearson's R = 0.91 C = log b = ± C oun t r y sc a li ng e x ponen t s Estimated from the empiricalrelation between and Estimated from the country scaling relations D Fig 2.
Country scaling relationships. (A) Scaling relation between total urban GDP ( Y ) and total urban population ( S ) forall countries in our data set. (B) Scaling law between the smallest city population of a country ( s min ) and the country’s urbanpopulation ( S ). (C) Scaling law between the largest city population of a country ( s max ) and the country’s urban population( S ). In these three panels, markers represent the values for each country and the dashed lines are the country scalingrelationships of Eqs. (8), (5), and (6), where the exponents γ , δ , and θ are obtained from fitting the model of Eq. (9) to theempirical relation between β and α . Only the constants Y , a and b are adjusted to data and their best fitting values areshown in the panels ( ± standard errors). (D) Comparison between estimates of the country scaling exponent obtained byfitting Eq. (9) to the empirical association between β and α (bars in dark colors) and by directly fitting the values of thecountry scaling relationships (bars in light colors, see Fig. 6 in S1 Appendix for the adjusted scaling laws). Error barsrepresent 95% bootstrap confidence intervals of the parameters. We notice that both approaches yield similar estimates,which are statistically indistinguishable in the cases of δ and θ . Simulating the association between both exponents
The level of variation in the relation between the exponents β and α (as well as in thecountry scaling relationships) is significantly high and hampers a more visualcomparison with our model. In addition to indicating that our description of theassociation between both exponents is far from perfect, these variations also reflectpossible estimation errors in the population and GDP values, errors related to thedefinition of city boundaries, and mainly errors associated with estimating the Zipf andurban scaling exponents (as data does not perfectly follow the Zipf’s and urban scalinglaws). As these errors emerge from different sources and do not seem to affect theassociation between β and α systematically, we have treated them as random variationsand investigated their role via an in silico experiment. As summarized in the Materialsand Methods, we have generated artificial data at the city level (city population s andcity GDP y values) by considering Zipf’s law (Eq. 1), urban scaling (Eq. 2), countryscaling relations (Eqs. 5 and 6), and our model (Eq. 9). These simulations take asinputs the real values of total urban population S and the exponent α of each countryto generate replicas of these urban systems (set of values of s and y ), from which we caninvestigate the relationship between β and α under different levels of variation in theurban and country scaling relations. To do so, we have fixed the variation intensity(that is, the standard deviation of Gaussian random variation around the scaling laws)in the simulated country scaling relations to a level comparable with the empirical data,and varied the variation intensity in the simulated urban scaling σ y in percentages ofthe value observed in the real data ( σ y = 100% means the standard deviation of thesimulation is equal to the standard deviation in the empirical values of β ).The first four panels of Fig. 3A show examples of simulated relationships (red circles)in comparison with empirical data (blue dots) for different values of σ y . As expected,the simulated relationship perfectly agrees with our model (Eq. 9) when there is norandom variation in the urban scaling. More importantly, we note that the scattering ofsimulated data becomes visually very similar to the empirical data as the intensity ofthe random variation increases up to σ y = 100% (Fig. 8 in S1 Appendix). We can alsouse the simulated data to corroborate our numerical experiment by verifying theJanuary 11, 2021 7/17ountry scaling relations. Figures 3B-D show the simulated country scaling relations incomparison with the behavior of Eqs. (5), (6), and (8) with parameters estimated fromreal data. We note that simulated scaling relations for total urban GDP ( Y ) andsmallest city population ( s min ) follow very closely the adjusted behavior of the empiricaldata.However, the simulated results for the largest city population ( s max ) systematicallyunderestimate the trend observed in the empirical data. This happens because, in oursimulations, we have used a random number generator associated with a truncatedpower-law distribution (between s min and s max ) for mimicking population valuesaccording to Zipf’s law. Since large populations are rare and the number of simulatedcities is finite, the simulated values for the largest city population do not get closeenough to the upper bound imposed by the truncated power-law distribution.Consequently, the simulated values of s max underestimate the empirical ones. We solvethis issue by replacing the truncated power-law behavior by a power-law distributionwith exponential cutoff (Materials and Methods). This modification does not alter thecountry scaling relations of total urban GDP and smallest city population, that is, theresults of Fig. 3B and 3C are not affected by the introduction of the exponential cutoff.Similarly, this modification does not affect the relationship between β and α and thesimulated associations with exponential cutoff are very similar to those obtained withthe truncated power-law (as indicated by the right-most plot in Fig. 3A). Indeed, theinclusion of this exponential cutoff only modifies the country scaling relation of thelargest city population by increasing the simulated values of s max . Figure 3E shows anexample of simulated results after after replacing the truncated cut-off with aexponential one for the country scaling relation between s max and S . We observe thatthe simulated values of s max obtained with the exponential cutoff are closer to theempirical data behavior than those obtained with the truncated power-law distribution(Fig. 3D). Discussion
We have shown that the combination of Zipf’s law and urban scaling implies a countryscaling relationship, where the exponent is a function of the Zipf and the urban scalingexponents. While the Zipf and the urban scaling exponents vary from country tocountry, there is only one country scaling exponent for a given indicator, which in turnimplies a direct association between the urban scaling and the Zipf exponents. Inqualitative terms, our results agree with the more holistic idea that urban scalingexponents do not solely emerge from processes occurring within the city boundaries;instead, cities do not represent a closed and non-interacting system and what happensin the entire system (such as flow of people and goods) may affect urban scaling.Similarly to what happens in transportation theory where the product of two cities’populations is usually assumed to be proportional to the commuting flow between them(such as in gravity models), the population of cities is likely to represent an importantfactor for the interactions among cities. Under this assumption, the distribution of citypopulation (summarized by the Zipf exponent) may thus represent an indirect proxy forinteractions between cities, and the association observed between β and α summarizeshow the population distribution affects urban scaling and vice versa.Theoretically, the connection between the exponents β and α would imply thatinstead of unrelated, Zipf’s law and urban scaling are indeed the two sides of the samecoin. However, the non-negligible variability observed in the empirical relationship donot corroborate with such a simple conclusion but suggest that other factors (such aslevel of socio-economic development and the particular history of an urban system)beyond population distribution may also have a significant effect on the urban scaling ofJanuary 11, 2021 8/17 .0 6.5 7.0 7.5 8.0 8.5 Country's urban population, log S U r ban G D P , l o g Y Pearson's R = 0.76 y =100 % = log Y = Country's urban population, log S S m a ll e s t c i t y popu l a t i on , l o g s m i n Pearson's R = 0.85 y =100 % = log a = Country's urban population, log S La r ge s t c i t y popu l a t i on , l o g s m a x Pearson's R = 0.92 y =100 % = log b = Country's urban population, log S La r ge s t c i t y popu l a t i on , l o g s m a x Pearson's R = 0.86 y =100 %(exponential cutoff) = log b = Zipf exponent, U r ban sc a li ng e x ponen t, y = Zipf exponent,
Empirical data y = Zipf exponent, y = Zipf exponent, y = Zipf exponent, y = AB C D E = 1= = = = Fig 3.
Simulating the connection between α and β , and the country scaling relationships. (A) Simulated relationshipsbetween α and β under different levels of random variation in the urban scaling law (Eq. 2). Here σ y is the percentage of thestandard deviation in the empirical values of β . We have a perfect agreement between simulations and the model of Eq. (9)when σ y = 0%, and the results become very similar to the empirical data (small blue dots) as the intensity of the randomvariation increases. (B)-(D) Simulated country scaling laws for σ y = 100%. The dashed lines represent the scalingrelationships of Eqs. (8), (5), and (6), with parameters estimated from empirical data. We notice that the simulated scalinglaws of total urban GDP ( Y ) and smallest city population ( s min ) follow well the empirically adjusted relationships, while thesimulated values for the largest city population ( s max ) underestimate the empirical values. This occurs because largepopulations are rare and do not get close enough to the imposed maximum s max . (E) Scaling relationship between s max and S when considering that city population values are drawn from a power-law distribution with exponential cutoff. We noticethis change makes the simulated results very similar to the empirical ones. The right-most plot in panel A shows a simulatedrelation between β and α when considering the exponential cutoff.GDP. Understanding the relative importance of population distribution on urbanscaling (and vice versa) for different indicators is an important future contribution thatis currently limited by the availability of other world-wide comparable city indicators.Even when considering the unexplained variation in the data, the connection betweenthe two scaling laws uncovered by our work indicates the existence of universalprocesses governing both laws; however, finding out this commonality for arbitraryurban indicators still represents a challenging task.In the context of urban GDP, our results show that urban systems with small valuesof the Zipf exponent also tend to present lower increasing returns to scale of GDP (lowvalues of β ). An urban system described by a small Zipf exponent has a more balancedpopulation distribution, and consequently, fewer small cities and more large cities whencompared with urban systems described by larger Zipf exponents. Thus, countries withproportionally more metropolises tend to have less pronounced increasing returns toscale than those having a small number of large cities. We hypothesize that urbansystems with a large number of metropolises may also have a more integrated marketwhereby these large cities cooperate and develop specialized economic activities. As aresult, urban systems with more metropolises would have a smaller degree ofagglomeration of economic activities in large cities and so weaker increasing returns toscale for city GDP. In contrast, countries with a small number of large cities have toconcentrate almost all complex economic activities in relatively fewer metropolises,which in turn intensifies the increasing returns to scale of urban GDP (high values of β ).January 11, 2021 9/17t is also interesting to note that high-GDP countries present relatively smallervalues of Zipf and urban scaling exponents than mid-GDP and low-GDP countries(Fig. 1A and Fig. 9 in S1 Appendix), that is, developed countries tend to have moremetropolises and less pronounced increasing returns to scale of urban GDP. This latterpoint agrees with the more local observation that “rich cities” of the European Union(West cities) also exhibit smaller scaling exponents for GDP than their “poor”counterparts (East cities) [27]. Large values of β may express an urban system withhigh economic performance, but because β alone does not define the total urban GDP,large values of β also indicate a significant imbalance between the economic productivityof small and large cities. The association between β and α also suggests that part ofthis economic inequality may reflect the unbalanced distribution of population. It isalso worth mentioning the possibility of the existence of different urban planningregimes [45] that may prevent sharp population agglomerations in developed countriesand thus also partially explain the negative association between β and total urban GDP.Our data do not allow a dynamic analysis nor the identification of the causaldirection of the association between the exponents β and α . Still, a possible explanationfor the observed differences among countries with different levels of development is thatthe economic policies in less developed countries have focused on large cities, fosteringthis unbalanced situation and creating cities larger than an hypothetical economicallyoptimal. From a labor-market perspective, these large cities may attract inhabitantsfrom smaller cities, changing both the urban scaling and the Zipf exponents. However,these new inhabitants may mostly find low-paying jobs or even become unemployed,which in turn might partially explain the poorer overall economic performance of lessefficient urban systems. The association between both exponents is even more crucialbecause the world urban population may increase up to 90% by 2100 [46]. Thisurbanization process is likely to be even more intense in developing countries and hasthe potential to further undermine their economic performance. Thus, it is not onlyimportant to discuss which scaling is desirable but also the population distributionwithin urban systems. Materials and Methods
Data
The data used in this work is a product of two data sets. First, we use the recentlyreleased GHSL-FUA or eFUA [38, 39] definition of functional urban areas (FUAs). TheeFUAs uses gridded population data from Global Human Settlement Layer(GHSL) [47, 48] and an automated classification approach for producing 9,031 urbanboundaries (and population counts) over the entire globe (188 countries) for the year2015. The eFUAs comprise high-density urban centers and their surroundingcommuting zones and aim to capture the functional extent of cities. Second, we use thegridded GDP data provided by Kummu et al. [40]. This data set combines sub-nationaland national GDP data from different sources with population gridded data (from theGHSL and the HYDE 3.2 [49]) to define three gridded global datasets: Gross DomesticProduction per capita (5 arc-min resolution), Human Development Index (5 arc-minresolution), and Gross Domestic Production (30 arc-sec-min resolution). We have usedonly this latter file representing gridded values of total GDP with a resolution of 30arc-sec (1 km at equator) for the year 2015 (the same information is also available forthe years 1990 and 2000). To define GDP consistently at the grid level across countries,Kummu et al. first calculate the GDP across gridcells within each subnational unit of agiven country as the corresponding subnational GDP per capita value multiplied by thegridcell population. Next, the authors sum over these gridcell GDP values and divide byJanuary 11, 2021 10/17he sum gridcell populations in a country to define the population-weighted nationalGDP per capita. They then calculate the ratio between this population-weightednational GDP per capita and the subnational GDP per capita. Finally, they multiplythis ratio by the national GDP per capita to obtain the final subnational GDP percapita values (that vary across subnational units in each country), which they thenmultiply by the population in each gridcell within each subnational unit to obtain thefinal GDP for every gridcell in a given country. This method ensures that the sum overGDP per capita values at the gridcell level always coincides with officially reportedGDP per capita values for each country, and that there is global consistency becausethe method relies on secondary sources of reported subnational GDP per capita andinternationally consistent population grids. The gridded GDP values are reported in2011 international US dollars using purchasing power parity rates (total GDP-PPP). Weoverlay the gridded GDP data with eFUA boundary polygons and aggregate the GDPcell values within each polygon for associating a GDP value to each eFUA. We illustratethis procedure in Fig. 1 in S1 Appendix. Next, we group the resulting data by countryand select the countries having at least 10 eFUAs. We also removed from our analysis46 eFUA with null GDP (16 from India; 9 from Ethiopia; 5 from Pakistan; 3 fromSudan; 2 from Niger, Congo, and Chad; and 1 from Argentina, Benin, Egypt, Indonesia,Myanmar, Senegal, and Uganda). These criteria lead us to a data set comprisingpopulation s and GDP y of 8,650 functional urban areas from 96 countries. Estimating the Zipf exponent
Zipf’s law (Eq. 1) implies that the complementary cumulative distribution function(CDF) of city population is a power law, F ( s ) ∼ s − ζ , with ζ ≈ α . We use thisconnection to estimate the values of α from the data. Specifically, we applied theapproach of Clauset-Shalizi-Newman [50] to obtain the exponent α via its maximumlikelihood estimate α = n/ ( (cid:80) ni =1 ln s i / ˜ s min ) , where ˜ s min is the lower bound of thepower-law regime, s i is the population of the i -th city for a given country such that s i ≥ ˜ s min , and n is the number of city populations in the power-law regime. The valueof ˜ s min is also estimated from data by minimizing the Kolmogorov-Smirnov “distance”between the empirical CDF of city populations and F ( s ). The standard error in theZipf exponent SE α = α/ √ n can be obtained from the width of the likelihoodmaximum [50]. We have used the Clauset-Shalizi-Newman method as implemented inthe Python module powerlaw [51]. In addition to being a quite popular approach forfitting power-law distributions, Bhattacharya et al. [52] have recently proven that theClauset-Shalizi-Newman approach yields an unbiased and consistent estimator, that is,as data increases indefinitely the estimated parameters converge (in distribution) to thetrue values. We show the CDF and Zipf’s law adjusted to each country in S1 Appendix,Sec. 4, where a good agreement is observed in the vast majority of cases. Afterestimating ˜ s min , we filter out all cities with population smaller than this threshold in allother analyses, leading us to 4,571 functional urban areas from 96 countries. Thus, theurban scaling laws involve only cities belonging to the power-laws regime, and thecountries’ urban GDP ( Y ) and countries’ urban population ( S ) are the aggregatedvalues of urban GDP ( y i ) and urban population ( s i ) of cities belonging to the power-lawregime for each country. Estimating the urban scaling and the country scaling exponents
Urban scaling and country scaling laws are generically represented by a power-lawrelation between a dependent variable z and an independent variable xz = g x ν , (10)January 11, 2021 11/17here g is a prefactor and ν is the power-law exponent. Equation (10) is linearized via alogarithmic transformation log z = log g + ν log x , (11)where log z and log x now represent the dependent and independent variables, log g isthe intercept and ν the slope, both being regression coefficients of a correspondinglinear model. We have estimated the values of log g and ν by adjusting Eq. (11) to thelog-transformed data via robust linear regression with the Huber loss function [53], asimplemented in the Python module statsmodels [54]. We further estimate standarderrors and confidence intervals for the parameters log g and ν via bootstrapping [55].We show the urban scaling law adjusted to each country in S1 Appendix, Sec. 4, wherea good agreement is observed in the vast majority of cases. The adjusted countryscaling laws are shown in Fig. 6 in S1 Appendix. In the case of Figs. 2A-C, we havefixed the power-law exponents (regression coefficients) γ , δ and θ to values obtainedfrom fitting Eq. (9) to the relation β versus α , and only the prefactors (intercepts of thelinear model) log Y , log a , and log b have been considered as free parameters in theregression model. Fitting our model to the relationship between β and α Our model for the relationship between β and α is completely defined in S1 Appendix,Sec. 2. Depending on whether γ > γ < δ < θ or δ > θ , wehave an expression of β as function of α (Eqs. S56-S59, in S1 Appendix) and Eq. (9) isa particular case when γ > δ < θ . We have adjusted the complete model (that is,without assuming anything about the parameters γ , δ , and θ ) to the empirical relationbetween α and β via the L-BFGS-B nonlinear optimization algorithm [56], asimplemented in the Python module lmfit [57] and without any constraint. Thestandard errors and the confidence intervals on the parameters γ , δ and θ are estimatedvia bootstrapping [55]. The best fitting parameters ( ± standard errors) are γ = 1 . ± . δ = 0 . ± .
05, and θ = 0 . ± .
03. This leads to Eq. (9) because thebest fitting parameters yield γ > δ < θ . Figures 10, and 11 in S1 Appendix depictdifferent versions of Fig. 1A where we label all countries and show the standard errorsin β and α . Simulating relations between β and α We simulate the relationship between β and α by generating data at the city level. Fora given country population P with Zipf exponent α , we start by generating a list of m city populations S = { s , . . . , s i , . . . , s m } until satisfying the constraint (cid:80) mi =1 s i ≈ S N (0 ,σ γ ) , where N (0 , σ γ ) is a Gaussian random variable with zero meanand standard deviation σ γ . Each s i is drawn from a power-law distribution p ( s ) ∼ s − ( α +1) (compatible with Zipf’s law) within the interval s min < s < s max , where s min and s max are obtained from the country scaling relations (Eqs. 5 and 6) withmultiplicative random variations, that is, s min ∼ S δ N (0 ,σ δ ) and s min ∼ S θ N (0 ,σ θ ) ,where N (0 , σ δ ) and N (0 , σ θ ) are Gaussian random variables with zero mean andstandard deviations σ δ and σ θ , respectively. We next generate a list of urban indicators Y = { y , . . . , y i , . . . , y m } , where y i = c s βi N (0 ,σ y ) and N (0 , σ y ) is a Gaussian randomvariable with zero mean and standard deviation σ y . In the expression for y i , the valueof β is obtained from our model (Eq. 9) while the value of c is chosen to satisfy thecondition (cid:80) mi =1 y i ≈ Y , where Y is the total urban GDP (S1 Appendix, Sec. 3). Therandom variation controlled by the parameters σ γ , σ δ , and σ θ mimics the variabilityobserved in the empirical country scaling relationships, and we set their values equal tothe standard deviation of the bootstrap estimates of the country scaling exponents ( γ , δ ,January 11, 2021 12/17nd θ ). On the other hand, the random variation controlled by σ y mimics the variabilityin the urban scaling relationships, and we set its value as a fraction of the standarddeviation of the empirical values of β . We have thus applied this procedure by using allempirical values of α and Y to obtain the simulated values of β , Y , s min , s max from thelists S and Y under different values of σ y (Fig. 3A).We have also considered a modification of this procedure where the populationvalues were drawn from a power-law distribution with exponential cutoff [50], that is, p ( s ) ∼ s − ( α +1) exp( − s/s ) ( s > s min ), where s is an additional parameter. Thismodification is necessary for reproducing the empirical behavior of the country scalingbetween s max and S . Because large city populations are very rare, the simulated valuesof s i obtained from the upper-truncated power-law distribution do not get close enoughto the imposed maximum value ( s max ). This results in the underestimation of s max , asshown in Fig. 3D. After replacing the upper-truncated behavior by the exponentialcutoff, we note that the simulated country scaling of s max becomes very similar to theempirical relation (Fig. 3E). In this simulation, we have chosen the value s = 3 × tomake the simulated values of s max closer to the scaling law adjusted from the empiricaldata. It is worth mentioning that this change has no effect on the relationship between β and α nor on the other country scaling relations (see the two right-most plots ofFig. 3A).S1 Appendix, Sec. 3 shows more details on how we have implemented this simulation. Acknowledgments
We thank K. Schmidheiny, J. Suedekum, and S. Thies for useful discussions. This workemerged from ideas discussed at the symposium
Cities as Complex Systems (Hanover,July 13th-15th, 2016) which was generously funded by VolkswagenFoundation. HVRacknowledges the support of CNPq (Grants Nos. 440650/2014-3 and 303642/2014-9).DR thanks the Alexander von Humboldt Foundation for financial support under theFeodor Lynen Fellowship. DR is also grateful to the Leibniz Association (projectIMPETUS) for financially supporting this research.
Supporting information
S1 Appendix. Supplementary Figures (1-11) and Supplementary Text(Sections 1-4) supporting the results discussed discussed in the main text.
References
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Association between population distribution and urban GDPscaling
H. V. Ribeiro ∗ , M. Oehlers, A. I. Moreno-Monroy, J. P. Kropp, D. Rybski ∗∗ Corresponding authors. E-mail: hvr@dfi.uem.br or [email protected] upplementary Figures
Gridded Log(GDP)
FIG. 1.
Illustration of the procedure used for obtaining population s and GDP y ofcities over the entire globe. The world map shows the boundaries of GHSL-OECD Func-tional Urban Areas (GHS-FUA or eFUA). This definition of urban areas has been recently re-leased by the European Commission’s science and knowledge service, with the aim of providingan internationally-comparable and harmonized definition of urban areas. The eFUA definitiondoes not rely on local administrative boundary units and commuting flows data; instead, it usesgridded data from the Global Human Settlement Layer (GHSL) and an automated classificationapproach for producing urban boundaries [JRC Tech. Rep. (2019) and J. Urban. Econ., 103242(2020)]. The shape file is provided for the year of 2015 together with population values for eacheFUA. We combine eFUA boundary data with gridded GDP data provided by Kummu et al. [Sci.Data 5, 180004 (2018)]. In more detail, we use the total GDP-PPP (purchasing power parity, inconstant 2011 international USD) data with 30 arc-sec resolution ( ≈ GDP PPP 30arcsec v2.nc ) for the year 2015 to overlay with eFUA boundaries. Next, we aggregateall grid cell values within each eFUA boundary to associate a GDP value to each urban area of theworld. We illustrate this idea by highlighting a small area in the southern part of Brazil, where wealso plot the GDP grid cells. .5 1.0 1.5 2.0 2.5 Zipf exponent, F r equen cy A Urban scaling exponent, F r equen cy B FIG. 2.
Probability distributions of the Zipf exponent α and the urban scaling exponent β . (A) The bars represent a histogram for the values of α and the continuous line is a kernel densityestimation (not normalized) for the same data. The vertical dashed line indicates the value α = α are 1.24 and 0.38, respectively. (B) The barsrepresent a normalized histogram for the values of β and the continuous line is a kernel densityestimation (not normalized) for the same data. The vertical dashed line indicates the value β = β are 1.16 and 0.17, respectively. .8 1.0 1.2 1.4 Center of Zipf exponent window, S pea r m an r an k c o rr e l a t i on , r A Center of Zipf exponent window, P ea r s on c o rr e l a t i on , B FIG. 3.
Correlation between the urban scaling exponent β and the Zipf exponent α over sliding windows of values of α . (A) Spearman rank correlation ( ρ r ) of the relationshipbetween β and α estimated within a sliding window centered in α ′ . (B) Pearson correlation ( ρ )of the relationship between β and α estimated within a sliding window centered in α ′ . For bothcorrelation measures, the size of sliding windows is ∆ α ′ = . p -values smaller than 0 . p -values larger than 0 . α ′ between 0.15 and 0.55. In bothpanels, the continuous black lines around zero represent average values of the correlation measuresestimated after shuffling the values of β (1000 realizations), and the gray shaded region stands forthe 95% bootstrap confidence intervals. We notice that the correlation measures are larger andstatistically significant for values α ′ around 1.1 and that the significant values cannot be explainedby the distribution of β values. This range containing the largest and significant values of ρ and ρ r mostly correspond with mid-range of α values in Eq. (9) [Eq. S56 in Supplementary Text], whereour model predicts a linear association between β and α (see main text for details). A I C and B I C A I C = A I C c o n s t - A I C m o d e l B I C = B I C c o n s t - B I C m o d e l A I C > and B I C > S t r ong o r v e r y s t r ong e v i den c e f o r ou r m ode l FIG. 4.
Comparison between the model of Eq. (9) [Eq. S56 in Supplementary Text] anda constant (intercept-only) model ( β = const). The left bar shows the difference between theAIC (Akaike information criterion) values (∆AIC) estimated for an intercept-only model (AIC const )and for the model of Eq. (9) [Eq. S56 in Supplementary Text] (AIC model ). The model with thelowest AIC value gives a better description of the data. Thus, ∆AIC > < ∆AIC <
10 as a strong evidence and ∆AIC ≥
10 as a very strong evidence(our case, since ∆AIC ≈ .
4) in favor of the model of Eq. (9) [Eq. S56 in Supplementary Text].In addition, because the AIC value is proportional to the negative of log-maximum-likelihood ofthe model, the quantity e ∆AIC approximates how more likely the model of Eq. (9) [Eq. S56 inSupplementary Text] is to describe the data when compared with an intercept-only model. Thus,we notice that Eq. (S56) is ≈ β and α than the intercept-only model. The right bar shows the difference between the BIC (Bayesianinformation criterion) values (∆BIC) estimated for an intercept-only model (BIC const ) and forthe model of Eq. (9) [Eq. S56 in Supplementary Text] (BIC model ). The interpretation of BICand AIC values are analogous. The results indicate a strong evidence (∆BIC ≈ .
3) in favor ofEq. (9) [Eq. S56 in Supplementary Text] and our model is ≈
103 times more likely to describe theempirical data than the intercept-only model. It is worth remembering that both AIC and BICvalues account for the fact that Eq. (9) [Eq. S56 in Supplementary Text] has more free parametersthan the intercept-only model (3 versus 1 parameter); moreover, BIC values penalize the numberof parameters more heavily. .00.10.20.30.40.50.6 S pea r m an r an k c o rr e l a t i on , r Lo w p l a t eau r eg i on ( ) L i nea r r eg i on ( < < * ) H i gh p l a t eau r eg i on ( * ) * p -value =0.125 p -value =0.001 p -value =0.078 P ea r s on c o rr e l a t i on , Lo w p l a t eau r eg i on ( ) L i nea r r eg i on ( < < * ) H i gh p l a t eau r eg i on ( * ) * p -value =0.032 p -value =0.003 p -value =0.009 A B
FIG. 5.
Correlations in each range of values of α defined in Eq. (9) [Eq. S56 in Supple-mentary Text] . (A) Spearman rank correlation ρ r between β and α in the low plateau ( α ≤ < α < α ∗ ), and high plateau ( α ≥ α ∗ ) regions of Fig. 1 in the main text. Panel (B)shows the same for the Pearson correlation coefficient ρ . In both panels, we indicate above the barsthe p -values testing the significance of the correlation coefficient (permutation test). We notice that ρ r and ρ are significantly higher in the linear region. We further observe that the correlations arestatistically significant at 99% confidence level only in the linear region. Here α ∗ = + γ − δ ≈ . .5 7.0 7.5 8.0 8.5 Country population, log S U r ban G D P , l o g Y A = ± log Y = ± Country population, log S S m a ll e s t c i t y popu l a t i on , l o g s m i n B = ± log a = ± Country population, log S La r ge s t c i t y popu l a t i on , l o g s m a x C = ± log b = ± FIG. 6.
Fitting country scaling relationships directly to data. (A) Scaling relation betweentotal urban GDP of countries ( Y ) and country’s urban population values ( S ). (B) Scaling lawbetween the smallest city population of a country ( s min ) and country’s urban population ( S ). (C)Scaling law between the largest city population of a country ( s max ) and country’s urban population( S ). In the three panels markers represent the values for each country and the dashed lines are thecountry scaling relationships of Eqs. (8), (5), and (6) [Eqs. (S6), (S7), and (S8) in SupplementaryText], where the exponents γ , δ , and θ (and the prefactors log Y , log a , and log b ) are obtainedvia robust linear regression of the log-transformed data. The best fitting parameters are shownin the panels ( ± standard errors) and gray shaded regions stand for the 95% confidence band ofthe models. As discussed in the main text, the exponents estimated directly from the scaling lawsare very similar to the values obtained by fitting Eq. (9) [Eq. S56 in Supplementary Text] to therelationship between β and α (see Fig. 2D of main text for a comparison).
10 20 30 40 50
GDP percentile threshold, %GDP * C oun t r y sc a li ng e x ponen t s A GDP percentile threshold, %GDP * A I C = A I C c o n s t - A I C m o d e l AIC >6 Strong or very strong evidence for our model B GDP percentile threshold, %GDP * B I C = B I C c o n s t - B I C m o d e l BIC >6 Strong or very strong evidence for our model C FIG. 7.
Robustness of the model of Eq. (9) [Eq. S56 in Supplementary Text] againstdifferent GDP threshold. (A) The colored markers show the values of γ , δ , and θ estimatedby fitting (via the L-BFGS algorithm) Eq. (9) [Eq. S56 in Supplementary Text] to the relationshipbetween β and α after selecting countries with total urban GDP higher than the percentile GDPthreshold (%GDP ∗ ). The shaded regions are 95% bootstratp confidence intervals and the dashedlines represent the values when considering all data. We notice the exponent estimates are quitestable. (B) Difference between the AIC (Akaike information criterion) values (∆AIC) estimatedfor an intercept-only model (AIC const ) and for the model of Eq. (9) [Eq. S56 in SupplementaryText] (AIC model ) as a function of the percentile GDP threshold (%GDP ∗ ). (C) Difference betweenthe BIC (Bayesian information criterion) values (∆BIC) estimated for an intercept-only model(BIC const ) and for the model of Eq. (9) [Eq. S56 in Supplementary Text] (BIC model ) as a functionof the percentile GDP threshold (%GDP ∗ ). Results show strong evidence (∆AIC > > .4 0.2 0.0 0.2 0.4 Fluctuations around the model P r obab ili t y d i s t r i bu t i on EmpiricalSimulations with x =100%Simulations with x =100%(exponential cutoff) FIG. 8.
Probability distributions of the random variations around the model of Eq. (9)[Eq. S56 in Supplementary Text].
The different curves show kernel density estimations ofthe random variations around the model of Eq. (9) when considering the empirical data andthe simulations obtained for σ y =
10 11 12 13
Urban GDP, log Y Z i p f e x ponen t, A slope = -0.11 ± p -value = 0.002) Urban GDP, log Y U r ban sc a li ng e x ponen t, B slope = -0.07 ± p -value = 0.000) FIG. 9.
Association between the exponents α and β and total urban GDP Y . (A) Scatterplot of Zipf exponent α versus the total urban GDP Y . (B) Scatter plot of urban scaling exponent β versus the total urban GDP Y . The dashed line in each panel represents a linear regression withslope indicated within the plots (where we also shoe the Pearson correlation coefficient and thecorresponding p -values). We observe that both exponents also significantly associated with urbanGDP Y , such that an increase in Y tends to be followed by a decrease in α and β . .5 1.0 1.5 2.0 2.5 3.0 Zipf exponent, U r ban sc a li ng e x ponen t, AFGAGOARGAUS AZE BDIBEL BEN BFABGDBLRBOL BRACAN CHECHLCHN CIVCMR CODCOL CUBCZEDEUDOM DZAECUEGY ESP ETHFRAGBRGHAGINGRC GTMHND HTI HUNIDN INDIRN IRQITA JPN KAZKENKOR LBYLKA MAR MEXMLI MMR MOZMYSNER NGA NICNLDNPL OMNPAK PERPHLPOL PRK ROURUSSAU SDNSEN SOMSRB SSDSWESYR TCDTGOTHATJK TKMTUNTURTWN TZA UGA UKRUSAUZB VENVNMYEMZAF ZMBZWE = ± = ± = ± AGOARG AZEBEL BEN BGDBLRBOL BRACAN CHECHLCHN CIVCMR CODCOL CZEDEUDOM ECUESP FRAGBR GHAGINGRC HND HTIIDN INDIRNITA JPN KENKOR LBYLKA MAR MEXMLI MMRNER NGA NLDOMNPAK PERPHLPOLSAU SDNSEN SRB SWESYR TGOTHATJKTUN TUR TZA UGAUSA UZB VENVNMYEMZAF ZWE = 1=
FIG. 10.
Association between the urban scaling exponent β and the Zipf exponent α . The markers indicate the values of β versus α for each country in our data set. The three markercolors group countries according to the tercile values of the total urban GDP distribution (forinstance, High-GDP countries have highest ≈
33% GDP values, as the main text). The horizontaldashed line shows the β =
1, while the inclined dashed line represents the β = α relationship. Thecontinuous line shows the model of Eq. (9) [Eq. S56 in Supplementary Text] adjusted to the dataand the gray shaded region stands for the 95% bootstrap confidence band. The colored shadedregions represent the different intervals of α defined in Eq. (9) [Eq. S56 in Supplementary Text].All countries are labeled according to their ISO codes (the three letters over each marker). Theblue frame indicates a region that has been magnified on the right. .5 1.0 1.5 2.0 2.5 3.0 Zipf exponent, U r ban sc a li ng e x ponen t, AFGAGOARGAUS AZE BDIBEL BEN BFABGDBLRBOL BRACAN CHECHLCHN CIVCMR CODCOL CUBCZEDEU DOM DZAECUEGY ESP ETHFRAGBR GHAGINGRC GTMHND HTI HUNIDN INDIRN IRQITA JPN KAZKENKOR LBYLKA MAR MEXMLI MMR MOZMYSNER NGA NICNLDNPL OMNPAK PERPHLPOL PRK ROURUSSAU SDNSEN SOMSRB SSDSWESYR TCDTGOTHATJK TKMTUN TURTWN TZA UGA UKRUSA UZB VENVNMYEMZAF ZMBZWE
AFGAGOARGAUS AZE BDIBEL BEN BFABGDBLRBOL BRACAN CHECHLCHN CIVCMR CODCOL CUBCZEDEUDOM DZAECUEGY ESP ETHFRAGBRGHAGINGRC GTMHND HTI HUNIDN INDIRN IRQITA JPN KAZKENKOR LBYLKA MAR MEXMLI MMR MOZMYSNER NGA NICNLDNPL OMNPAK PERPHLPOL PRK ROURUSSAU SDNSEN SOMSRB SSDSWESYR TCDTGOTHATJK TKMTUN TURTWN TZA UGA UKRUSA UZB VENVNMYEMZAF ZMBZWE = ± = ± = ± FIG. 11.
Association between the urban scaling exponent β and the Zipf exponent α . The same as Fig. (10) but with error bars indicating standard errors. The three colors groupcountries according to the tercile values of the total urban GDP distribution (for instance, High-GDP countries have highest ≈
33% GDP values). The horizontal dashed line shows the β =
1, whilethe inclined dashed line represents the β = α relationship. The continuous line shows the model ofEq. (9) [Eq. S56 in Supplementary Text] adjusted to data and the gray shaded region stands forthe 95% bootstrap confidence band. The colored shaded regions represent the different intervals of α defined in Eq. (9) [Eq. S56 in Supplementary Text]. All countries are labeled according to theirISO codes (the three letters over each marker). upplementary Text
1. CONNECTION BETWEEN URBAN SCALING AND ZIPF EXPONENTS
Let us start by considering an urban system (a country) composed of m cities with populations { s , s , . . . , s m } . Suppose now that we sort these pop-ulation values s in descending order { s max , . . . , s, . . . , s min } (where s max and s min are respectively the largest and smallest city population in the system)and associate a rank variable r defined by { , , . . . , r, . . . , m } to each citypopulation. Zipf’s law for cities states that rank r and city population s arerelated via r ∼ s − α , (S1)where α > F ( s ) canbe written as F ( s ) ∼ s − ζ , with ζ ≈ α , and, consequently, the probabilitydensity distribution P ( S ) of city population is P ( s ) ∼ s −( α + ) for s min < s < s max . (S2)From Eq. (S2) we can also write the frequency function or the absolutenumber of cities with population s as p ( s ) = ks −( α + ) for s min < s < s max , (S3)where k is a normalization constant determined by S = s max ∑ s = s min sp ( s ) ≈ k ∫ s max s min s − α ds (S4)and S is the total population of the urban system.On the other hand, the urban scaling hypothesis establishes a power-lawrelationship between an urban indicator y ( e.g. the urban GDP) and thepopulation s of a city, that is, y = cs β , (S5)where c is a positive constant, and β > β and α are related to each other, and e propose that the relationship between these two exponents emerge fromcountry scaling relationships.To derive the relationship between β and α , we consider S as the totalpopulation of an urban system and Y as the total quantity of the city in-dicator y for the whole urban system ( e.g. total urban GDP). It is worthnoticing that the values of S and Y represent the empirical values of totalpopulation and total GDP of all cities of a country within the power-lawregime (that is, all cities with population larger than the lower cutoff ob-tained after fitting the Zipf ’s law to the data, see Material and Methods inthe main text for details). In addition to the urban scaling that considersrelations between population and indicators of cities within one country, wefurther assume three different country scaling relations between populationand indicators across countries. The first one is a generalization of the urbanscaling hypothesis at the country level Y = Y S γ , (S6)where Y is a constant, and γ is the country scaling exponent associatedwith the indicator Y . The other two relationships relate the population ofthe smallest ( s min ) and largest ( s max ) cities in an urban system to the totalpopulation S, that is, s min = aS δ (S7) s max = bS θ , (S8)where a and b are positive constants, and δ > θ > s min and s max (Eqs. S7 and S8). Qualitatively speaking, we consider thatthe existence of country scaling relationships constrains the population andurban indicator values in a country which in turn ties the values of β and α .To find this connection, we notice that the total indicator Y can be ex- ressed by using Zipf’s law and urban scaling, that is, Y = s max ∑ s = s min yp ( s ) = s max ∑ s = s min cs β p ( s ) ≈ kc ∫ s max s min s β − α − ds . (S9)By determining the constant k from Eq. (S4) and solving the integral inEq. (S9), we should obtain the country scaling of Eq. (S6) in terms of theexponents α and β . Thus, if we assume γ , δ , and θ to be fixed, the changesin α and β must be constrained in order to yield the particular value of γ imposed by country scaling in Eq. (S6). Case A: α ≠ β ≠ α ≠ β ≠ k = ( α − ) Ss α max s α min s α max s min − s max s α min , (S10)and then by replacing s min with Eq. (S7) and s max with Eq. (S8), we find k = ( α − )( ab ) α SS ( δ + θ ) α ab α S δ + θα − a α bS θ + δα . (S11)By solving the integral in Eq. (S9), we find Y = kcβ − α ( s β − α max − s β − α min ) , (S12)and after replacing k by Eq. (S11), s min by Eq. (S7), and s max by Eq. (S8),we have Y = c ( α − ) Sα − β ( a β b α S δβ + θα − a α b β S θβ + δα ab α S δ + θα − a α bS θ + δα )= c ( α − ) Sα − β ( a β b α S λ − a α b β S λ ab α S λ − a α bS λ )= c ( α − ) Sα − β ( Λ − Λ Λ − Λ ) , (S13)where λ = δβ + θαλ = θβ + δαλ = δ + θαλ = θ + δα . (S14) nd Λ = a β b α S λ Λ = a α b β S λ Λ = ab α S λ Λ = a α bS λ . (S15)Because S represents the total population of an urban system or a country,we take the limit of large S in Eq. (S13). To do so, we need to know theconditions under which Λ dominates over Λ in the numerator of Eq. (S13),that is, when λ > λ δβ + θα > θβ + δα ( δ − θ )( β − α ) > , (S16)and also the conditions under which Λ dominates over Λ in the denominatorof Eq. (S13), that is, when λ > λ δ + θα > θ + δα ( δ − θ )( − α ) > . (S17)By investigating the inequality in Eq. (S16), we end up with the decisiontree of Figure 12. Similarly, we find the decision tree of Figure 13 for theinequality in Eq. (S17).Having the results of Figures 12 and 13, we can find the behavior of Y forlarge S in Eq. (S13) for each of the following conditions. > βδ > θ False and Λ dominates n o True and Λ dominates y e s n o δ < θ False and Λ dominates n o True and Λ dominates y e s y e s FIG. 12. Decision tree associated with the inequality λ > λ (Eq. S16) that defines whether Λ dominates over Λ (or vice-versa) in Eq. (S13). α > δ > θ False and Λ dominates n o True and Λ dominates y e s n o δ < θ False and Λ dominates n o True and Λ dominates y e s y e s FIG. 13. Decision tree associated with the inequality λ > λ (Eq. S17) that defines whether Λ dominates over Λ (or vice-versa) in Eq. (S13). Case A.1: α > β , α >
1, and δ < θ Under these conditions, we find that Λ and Λ dominate in Eq. (S13),yielding Y ≈ c ( α − ) a β − α − β S + λ − λ ≈ c ( α − ) a β − α − β S − δ + βδ . (S18)By comparing the result of Eq. (S18) with the country scaling in Eq. (S6),we find β = + γ − δ for { α > β & α > δ < θ } . (S19)It is worth noticing that the previous conditions depend on β , but by com- ining α > β & α > β , we can rewrite Eq. (S19) as β = + γ − δ for { α > max ( , + γ − δ ) & δ < θ } . (S20)Equation (S20) thus predicts that β is a constant, that is, not dependent on α when { α > max ( , + γ − δ ) & δ < θ } . Case A.2: α > β , α <
1, and δ < θ For this case, we find that Λ and Λ dominate the behavior of Eq. (S13)for large S , yielding Y ≈ c ( − α ) a β − α b α − α − β S + λ − λ ≈ c ( − α ) a β − α b α − α − β S − θ + βδ + α ( θ − δ ) . (S21)By comparing the previous result with Eq. (S6), we find β = γ + θ − δ + ( − θδ ) α for { α > β & α < δ < θ } , (S22)and after eliminating β from the condition, we have β = γ + θ − δ + ( − θδ ) α for { γ < + γ − θ < α < δ < θ } . (S23)Equation (S23) thus predicts a linear decreasing correspondence between β and α when { γ < + γ − θ < α < δ < θ } . Case A.3: α < β , α >
1, and δ < θ Under these assumptions, Λ and Λ dominate the behavior of Eq. (S13)for large S , leading to Y ≈ c ( α − ) a α − b β − α β − α S + λ − λ ≈ c ( α − ) a α − b β − α β − α S − δ + βθ + α ( δ − θ ) . (S24)By comparing the previous result with Eq. (S6), we find β = γ + δ − θ + ( − δθ ) α for { α < β & α > δ < θ } , (S25) hat after eliminating β from the condition leads to β = γ + δ − θ + ( − δθ ) α for { γ > < α < + γ − δ & δ < θ } . (S26)Similarly to Eq. (S23), the result of Eq. (S26) predicts a linear increasingcorrespondence between β and α when { γ > < α < + γ − δ & δ < θ } .It is worth noticing that the conditions underlying Eqs. (S23) and (S26)are mutually exclusive, that is, only one of the linear correspondences existsdepending on whether γ > γ < Case A.4: α < β , α <
1, and δ < θ For this case, we find that Λ and Λ dominate the behavior of Eq. (S13)for large S , resulting in Y ≈ c ( − α ) b β − β − α S + λ − λ ≈ c ( − α ) b β − β − α S − θ + βθ . (S27)By comparing the previous result with Eq. (S6), we find β = + γ − θ for { α < β & α < δ < θ } , (S28)and after eliminating β from the condition, we have β = + γ − θ for { α < min ( , + γ − θ ) & δ < θ } . (S29)Equation (S29) indicates that β is a constant when { α < min ( , + γ − θ ) & δ < θ } .If we assume that γ , δ and θ (with δ < θ ) are fixed, the combined behavior ofEqs. (S20), (S23), (S26), and (S29) produces a functional dependence of β on α composed by three continuous line segments: an initial horizontal plateau(Eq. S29) followed by an increasing (Eq. S26, when γ >
1) or decreasing(Eq. S23, when γ <
1) linear function followed by another horizontal plateau(Eq. S20). ase A.5: α > β , α >
1, and δ > θ Under these conditions, Λ and Λ dominate the behavior of Eq. (S13) forlarge S , yielding Y ≈ c ( α − ) b β − α − β S + λ − λ ≈ c ( α − ) b β − α − β S − θ + βθ . (S30)By comparing the previous result with Eq. (S6), we find β = + γ − θ for { α > β & α > δ > θ } , (S31)and after eliminating β from the condition, we have β = + γ − θ for { α > max ( , + γ − θ ) & δ > θ } . (S32)Equation (S32) thus predicts that β is a constant when { α > max ( , + γ − θ ) & δ > θ } . Case A.6: α > β , α <
1, and δ > θ For this case, Λ and Λ dominate the behavior of Eq. (S13) for large S and produce Y ≈ c ( − α ) a α − b β − α α − β S + λ − λ ≈ c ( − α ) a α − b β − α α − β S − δ + βθ + α ( δ − θ ) . (S33)By comparing the previous result with Eq. (S6), we find β = γ + δ − θ + ( − δθ ) α for { α > β & α < δ > θ } , (S34)and after eliminating β from the condition, we have β = γ + δ − θ + ( − δθ ) α for { γ < + γ − δ < α < δ > θ } . (S35)Equation (S35) predicts a linear decreasing correspondence between β and α when { γ < + γ − δ < α < δ > θ } . ase A.7: α < β , α >
1, and δ > θ For this case, Λ and Λ dominate the behavior of Eq. (S13), yielding Y ≈ c ( α − ) a β − α b α − β − α S + λ − λ ≈ c ( α − ) a β − α b α − β − α S − θ + βδ + α ( θ − δ ) . (S36)By comparing the previous result with Eq. (S6), we find β = γ + θ − δ + ( − θδ ) α for { α < β & α > δ > θ } , (S37)and after eliminating β from the condition, we have β = γ + θ − δ + ( − θδ ) α for { γ > < α < + γ − θ & δ > θ } . (S38)Equation (S38) predicts a linear increasing correspondence between β and α when { γ > < α < + γ − θ & δ > θ } . Similarly to cases A.2 and A.3,the conditions underlying Eqs. (S35) and (S38) are mutually exclusive, thatis, only one of the linear correspondences exists depending on whether γ > γ < Case A.8: α < β , α <
1, and δ > θ Under these conditions, Λ and Λ dominate the behavior of Eq. (S13),yielding Y ≈ c ( − α ) a β − β − α S + λ − λ ≈ c ( − α ) a β − β − α S − δ + βδ . (S39)By comparing the previous result with Eq. (S6), we find β = + γ − δ for { α < β & α < δ > θ } , (S40)and after eliminating β from the condition, we have β = + γ − δ for { α < min ( , + γ − δ ) & δ > θ } . (S41) quation (S41) predicts that β is a constant when { α < min ( , + γ − δ ) & δ > θ } .Similarly to cases A.1-A.4, the combined behavior of Eqs. (S32), (S35),(S38) and (S41) produces a functional dependence of β on α composed bythree continuous line segments: an initial horizontal plateau (Eq. S41) fol-lowed by an increasing (Eq. S38, when γ >
1) or decreasing (Eq. S35, when γ <
1) linear function followed by another horizontal plateau (Eq. S32).
Case B: α = β ≠ α = β ≠ β as function of α at α =
1. Under these assumptions,the normalization constant in Eq. (S4) is k = S ln ( s max s min ) , (S42)and by replacing s min and s max with Eqs. (S7) and (S8), we find k = S ln ( ba S θ − δ ) . (S43)The solution of the integral in Eq. (S9) for α = Y = kcβ − ( s β − − s β − ) , (S44)and after replacing k by Eq. (S43), s min by Eq. (S7), and s max by Eq. (S8),we find Y = cSβ − ⎛⎝ b β − S − θ + βθ − a β − S − δ + βδ ln ( ba S θ − δ ) ⎞⎠= cSβ − ⎛⎝ Ω − Ω ln ( ba S θ − δ ) ⎞⎠ , (S45)where Ω = b β − S − θ + βθ Ω = a β − S − δ + βδ . (S46) t is worth noticing that Eq. (S45) does not produce a “pure” power-law be-havior for large S due to the logarithmic function in its denominator. How-ever, the logarithmic function changes much slower than the power-law func-tions in the numerator, allowing us to approximate the behavior of Eq. (S45)by a power-law function for large S . β > δ > θ False and Ω dominates n o True and Ω dominates y e s n o δ < θ False and Ω dominates n o True and Ω dominates y e s y e s FIG. 14. Decision tree associated with the inequality in Eq. (S47) that defines whether Ω domi-nates over Ω (or vice-versa) in Eq. (S45). To estimate the behavior of Eq. (S45) for large values of S , we need todetermine the conditions under which Ω dominates over Ω , that is, when − θ + βθ > − δ + βδ ( δ − θ )( − β ) > . (S47)The inequality in Eq. (S47) leads us to the decision tree of Figure 14, andfrom these results, we can find the behavior of Y for large S in Eq. (S45) foreach of the following conditions. Case B.1: β > δ < θ Under these conditions, Ω dominates the behavior of Eq. (S45) for large S , leading us to Y = cb β − β − ⎛⎝ S − θ + βθ ln ( ba S θ − δ ) ⎞⎠ . (S48)By comparing the previous result with Eq. (S6) and considering that γ = − θ + βθ , we find β = + γ − θ for { α = β > δ < θ } . (S49) his result is the same as obtained for case A.4 and ensures the continuityof the behavior of β as a function of α at the point α = Case B.2: β < δ < θ For this case, Ω dominates the behavior of Eq. (S45) for large S , leadingto Y = ca β − − β ⎛⎝ S − δ + βδ ln ( ba S θ − δ ) ⎞⎠ . (S50)By comparing the previous result with Eq. (S6) and considering that γ = − δ + βδ , we find β = + γ − δ for { α = β < δ < θ } . (S51)This result is the same as obtained for case A.1 and ensures the continuityof the behavior of β as a function of α at the point α = Case B.3: β > δ > θ For this case, Ω dominates the behavior of Eq. (S45) for large S , leadingus to Y = − ca β − β − ⎛⎝ S − δ + βδ ln ( ba S θ − δ ) ⎞⎠ . (S52)It is worth noticing that Eq. (S52) yields positive values for Y since thelogarithmic function is negative when δ > θ and for large S . By comparingthe previous result with Eq. (S6) and considering that γ = − δ + βδ , we find β = + γ − δ for { α = β > δ > θ } . (S53)This result is the same as obtained for case A.8 and ensures the continuityof the behavior of β as a function of α at the point α = Case B.4: β < δ > θ For this case, Ω dominates the behavior of Eq. (S45) for large S , leadingus to Y = − cb β − − β ⎛⎝ S − θ + βθ ln ( ba S θ − δ ) ⎞⎠ . (S54) t is worth noticing that Eq. (S54) yields positive values for Y since thelogarithmic function is negative when δ > θ and for large S . By comparingthe previous result with Eq. (S6) and considering that γ = − θ + βθ , we find β = + γ − θ for { α = β < δ > θ } . (S55)This result is the same as obtained for case A.5 and ensures the continuityof the behavior of β as a function of α at the point α = . FUNCTIONAL DEPENDENCE BETWEEN URBAN SCALING AND ZIPFEXPONENTS At this point, we can combine the results of cases A1-A8 and write thefunctional dependence of β on α for each of the following conditions. For γ > δ < θ : By combining the cases A.1, A.3 and A.4, we find β = ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ + γ − θ < α ≤ γ + δ − θ + ( − δθ ) α < α < + γ − δ + γ − δ α ≥ + γ − δ . (S56)Equation (S56) represents three continuous line segments: an initial horizon-tal plateau ( α ≤
1) followed by an increasing linear function (1 < α < + γ − δ )followed by another horizontal plateau ( α ≥ + γ − δ ) higher than the first one.Figure 15 illustrates the typical behavior of Eq. (S56). Zipf exponent, U r ban sc a li ng e x ponen t, = 1 + = + + ( ) = 1 + = 1 = 1 + == 1 > 1, < FIG. 15. Illustration of the relation between β and α when γ > δ < θ predicted by Eq. (S56). or γ > δ > θ : By combining the cases A.5, A.7 and A.8, we find β = ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ + γ − δ < α ≤ γ + θ − δ + ( − θδ ) α < α < + γ − θ + γ − θ α ≥ + γ − θ . (S57)Equation (S57) represents three continuous line segments: an initial horizon-tal plateau ( α ≤
1) followed by an increasing linear function (1 < α < + γ − θ )followed by another horizontal plateau ( α ≥ + γ − θ ) higher than the firstone. It is worth noticing that we can pass back and forth from Eq. (S56) toEq. (S57) by replacing δ by θ . Zipf exponent, U r ban sc a li ng e x ponen t, = 1 + = + + ( ) = 1 + = 1 = 1 + == 1 > 1, > FIG. 16. Illustration of the relation between β and α when γ > δ > θ predicted by Eq. (S57). or γ < δ < θ : By combining the cases A.1, A.2 and A.4, we find β = ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ + γ − θ < α ≤ + γ − θγ + θ − δ + ( − θδ ) α + γ − θ < α < + γ − δ α ≥ . (S58)Equation (S58) represents three continuous line segments: an initial horizon-tal plateau ( α ≤ + γ − θ ) followed by a decreasing linear function (1 + γ − θ < α <
1) followed by another horizontal plateau ( α ≥
1) lower than the first one.
Zipf exponent, U r ban sc a li ng e x ponen t, = 1 + = + + ( ) = 1 + = 1= 1 + == 1 < 1, < FIG. 17. Illustration of the relation between β and α when γ < δ < θ predicted by Eq. (S58). or γ < δ > θ : By combining the cases A.5, A.6 and A.8, we find β = ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩ + γ − δ < α ≤ + γ − δγ + δ − θ + ( − δθ ) α + γ − δ < α < + γ − θ α ≥ . (S59)Equation (S59) represents three continuous line segments: an initial horizon-tal plateau ( α ≤ + γ − δ ) followed by a decreasing linear function (1 + γ − δ < α <
1) followed by another horizontal plateau ( α ≥
1) lower than the firstone. It is worth noticing that we can pass back and forth from Eq. (S58) toEq. (S59) by replacing δ by θ . Zipf exponent, U r ban sc a li ng e x ponen t, = 1 + = + + ( ) = 1 + = 1= 1 + == 1 < 1, > FIG. 18. Illustration of the relation between β and α when γ < δ > θ predicted by Eq. (S59). or δ = θ = ϕ : By combining the results of Eqs. (S56), (S57), (S58), and(S59), we find β = + γ − ϕ for α > , (S60)regardless of γ > γ <
1. Thus, we have that β is constant for all valuesof α when δ = θ . It is also interesting to note that β = γ =
1, that is,an isometric country scaling implies in isometric urban scaling relationships.
For γ =
1: By combining the results of Eqs. (S56), (S57), (S58), and (S59),we find β = γ > γ <
1. Thus, constant returns to scale at the countrylevel imply in constant returns to scale at the city level for all values of α . . NUMERICAL SIMULATIONS OF THE CONNECTION BETWEEN URBANSCALING AND ZIPF EXPONENTS In order to understand how variations in the country scaling and urbanscaling relationships affect the exact expressions of Sec. 2, we have designed anumerical experiment to simulate the empirical relation between β and α . Webegin by generating data at the city level, that is, given the total population S , total indicator Y , and Zipf exponent α for a country, we generate a list of m population values S = { s , s , . . . , s i , . . . , s m } , (S62)where each s i is a random number drawn from a truncated power-law distri-bution within the interval ( s max , s min ) with exponent α + Y = { y , y , . . . , y i , . . . , y m } , (S63)where each indicator y i follows the urban scaling law (Eq. S5) with randonvariations y i = c s β ( α,γ,δ,θ ) i N ( ,σ y ) log y i = log c + β ( α, γ, δ, θ ) log s i + N ( , σ y ) , (S64)where c is a constant, β ( α, γ, δ, θ ) represents the functional relationship be-tween the urban scaling exponent and the Zipf exponent (defined by Eqs. S56-S59) for given values of γ , δ and θ ), and N ( , σ y ) is Gaussian random variablewith zero mean and variance σ y . The term N ( , σ y ) introduces random vari-ations into the urban scaling relationship, but has a small impact on thecountry scaling relationships. Thus, in order to account for random varia-tions in the country scaling relationships, we have included analogous termsinto Eqs. (S7) and (S8), that is, s min = a S δ N ( ,σ δ ) log s min = log a + δ log S + N ( , σ δ ) (S65)and s max = a S θ N ( ,σ θ ) log s max = log a + θ log S + N ( , σ θ ) , (S66) here N ( , σ δ ) and N ( , σ θ ) are Gaussian random variables with zero mean,and variances σ γ and σ δ , respectively. Finally, we have further consideredrandom variations in the country scaling relationship between Y and S byadding a random term to the total country population, that is, S → S N ( ,σ γ ) , (S67)where N ( , σ γ ) is a Gaussian random variable with zero mean and variance σ γ .In our simulations the values s i and y i should satisfy the constraints ∑ mi = s i ≈ S and ∑ mi = y i ≈ Y . We satisfy the first constraint by iterativelygenerating values of s i and appending to S until ∑ mi = s i ≤ S . To fulfill thesecond constraint, we define the values of c by comparing Eq. (S6) withresults of Case A (Eqs. S18, S21, S24, S27, S30, S33, S36, and S39), that is, c ( α, β, δ, θ, a, b, Y ) = Y × ⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩ α − β ( α − ) a β − for { α > β & α > δ < θ } α − β ( − α ) a β − α b α − for { α > β & α < δ < θ } β − α ( α − ) a α − b β − α for { α < β & α > δ < θ } β − α ( − α ) b β − for { α < β & α < δ < θ } α − β ( α − ) b β − for { α > β & α > δ > θ } α − β ( − α ) a α − b β − α for { α > β & α < δ > θ } β − α ( α − ) a β − α b α − for { α < β & α > δ > θ } β − α ( − α ) a β − for { α < β & α < δ > θ } , (S68)where the value of Y is obtained from the fit of Eq. (S6) to the empiricalrelationship between Y and S (Fig. 2 of main text).Algorithm 1 shows the numerical procedures used in our simulations. Thisalgorithm defines the function generate country data that takes the coun-try population ( S ), the power-law exponents ( α, γ, δ, and θ ), some otherconstants ( Y , a , and b ), and the parameters related to the intensity of therandom variations ( σ y , σ γ , σ δ , and σ θ ) as arguments and returns the simu-lated lists of populations S and urban indicators Y . Having these lists, weestimate the simulated exponent ˜ β in the same way we have proceeded withthe empirical data, that is, via robust linear regression of the relationship lgorithm 1 Algorithm for generating a list of city populations ( S ) and a list of urbanindicators ( Y ) for a country with total population S . ( S , Y ) = generate country data ( S, α, γ, δ, θ, Y , a, b, σ y , σ γ , σ δ , σ θ ) S = S N ( ,σ γ ) ▷ N ( µ, σ ) is Gaussian random variate with mean µ and variance σ s min = a S δ N ( ,σ δ ) s max = b S θ N ( ,σ θ ) ˜ S = S = []Y = [] β = β ( α, γ, δ, θ ) ▷ Defined from Eqs. (S56), (S57), (S58), and (S59) c = c ( α, β, δ, θ, a, b, Y ) ▷ Defined from Eq. (S68) while ˜ S < S do s i = P( α + , s min , s max ) ▷ P( ν, x min , x max ) is power-law random variate ▷ with exponent ν in the interval ( x min , x max ) y i = c s βi N ( ,σ y ) ˜ S = ˜ S + s i S ←— s i ▷ Appends s i to the list of city populations SY ←— y i ▷ Appends y i to the list of city indicators Y end while log y i versus log s i . We also obtain the simulated values for total population˜ S and total indicator ˜ Y by summing up the values of s i and y i . Similarly, weestimate the simulated values of ˜ s min and ˜ s max by taking the maximum andminimum values within the list S .For our simulations, we use the total population (of all cities within thepower-law regime) of each country in our data set as values of S . For each ofthese values of S , we also use the corresponding estimated Zipf exponents α .In addition, we set up the values γ , δ , and θ equal to the best fitting valuesof the empirical relationship between β and α . The constants Y , a , and b donot affect the relationship between ˜ α and ˜ β , and have been chosen to matchthe fitted values obtained from the country scaling relationships (with fixedpower-laws exponents). We also set the parameters σ γ , σ δ and σ θ equal to thestandard deviations of the bootstrap estimates of the empirical exponents γ , δ , and θ , respectively. Finally, we have varied the parameter σ y and obtainedthe simulated relationship between ˜ β and ˜ α . The same approach is usedwhen considering that s i follows a power-law distribution with exponential utoff, that is, p ( s ) ∼ s −( α + ) exp (− s / s c ) (S69)where s c > P ( α + , s min , s max ) in Algorithm 1 by an a random number generator associ-ated with Eq. (S69), that is, a P ( α + , s min , s c ) . .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Afghanistan (AFG) = ± s min = City population, log s C i t y r an k , l o g r Kabul
Herat
Kandahar
Mazar i sharif
Jalalabad
Puli Khumri
Kunduz
Lashkar Gah
Taloqan
Charikar
Guzarah
Sar-e Pol
Ghazni
Shindand
Sheberghan
Girishk
Farah
Mihtarlam
Samangan
Khost
Khanabad
Bagram
Maymana
Chaman
Pul-i-Alam
Qala i Naw
Afghanistan (AFG) = ± s min = City population, log s C i t y G D P , l o g y Kabul
Herat
Kandahar
Mazar i sharif
Jalalabad
Puli Khumri
Kunduz
Lashkar Gah
Taloqan
Charikar
Guzarah
Sar-e Pol
Ghazni
Shindand
Sheberghan
Girishk
Farah
Mihtarlam
Samangan
Khost
Khanabad
Bagram
Maymana
Chaman
Pul-i-Alam
Qala i Naw
Afghanistan (AFG) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Angola (AGO) = ± s min = City population, log s C i t y r an k , l o g r Luanda
Lubango
Huambo
Cabinda
Benguela
Malanje
Lobito
Uíge
Kuito
Saurimo
Luena
Ondjiva
Menongue
Namibe
Cubal
Matala
Bailundo
Ganda
Andulo
Calilongue
Sumbe
Dundo
N'dalatando
M'banza Congo
Camacupa
Caconda
Gabela
Waku Kungo
Soyo
Katchiungo
Quipungo
Cafunfo
Cazombo
UNNAMED
Catabola
Vila Nova do Seles
Porto Amboim
Chinguar
Luau
Caxito
Bocoio
Balombo
Angola (AGO) = ± s min = City population, log s C i t y G D P , l o g y Luanda
Lubango
Huambo
Cabinda
Benguela
Malanje
Lobito
Uíge
Kuito
Saurimo
Luena
Ondjiva
Menongue
Namibe
Cubal
Matala
Bailundo
Ganda
Andulo
Calilongue
Sumbe
Dundo
N'dalatando
M'banza Congo
Camacupa
Caconda
Gabela
Waku Kungo
Soyo
Katchiungo
Quipungo
Cafunfo
Cazombo
UNNAMED
Catabola
Vila Nova do Seles
Porto Amboim
Chinguar
Luau
Caxito
Bocoio
Balombo
Angola (AGO) = ±
4. ZIPF AND URBAN SCALING PLOTS FOR EACH COUNTRY
In this section, we show Zipf ’s law and urban scaling law adjusted forevery country in our data set. In what follows, each row of panels showsthe results for a given country (name is indicated within the plots). Thefirst column shows the complementary cumulative distribution F ( s ) of citypopulation s (gray continuous line) and the adjusted power-law distribution(dashed line). The second column shows the rank plot, where each city isnamed within the plots. The dashed lines show the adjusted Zipf’s law. Thepower-law exponent α ( ± standard error) and the lower cutoff populationsize s smin ( ± standard error) are estimated from the approach of Clauset-Shalizi-Newman [SIAM Review 51, 661 (2009)]. The third column showsurban scaling between urban GDP and city population, where each city isalso named within the plots. The dashed line represents the adjusted scalinglaw. The urban scaling exponent β ( ± standard error) is estimated via robustlinear regression on the log-transformed quantities. .0 5.5 6.0 6.5 7.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Argentina (ARG) = ± s min = City population, log s C i t y r an k , l o g r Buenos Aires
Cordoba
Rosario
Mendoza
San Miguel de Tucumán
La Plata
Mar del Plata
Salta
San Juan
Santa Fe
Santiago del Estero
Resistencia
Neuquén
Corrientes
Posadas
San Salvador de Jujuy
Bahía Blanca
Paraná
Formosa
San Fernando del Valle de Catamarca
Comodoro Rivadavia
San Luis
La Rioja
Zárate
San Rafael
San Nicolás de los Arroyos
Concordia
Río Cuarto
San Martín
Tandil
Villa Mercedes
San Carlos de Bariloche
Reconquista
Río Gallegos
Santa Rosa
Luján
Presidencia Roque Sáenz Peña
General Roca
Trelew
Villa María
Villa Carlos Paz
Puerto Madryn
Rafaela
San Ramón de la Nueva Orán
Oberá
Goya
Pergamino
Junín
Gualeguaychu
Necochea
Viedma
Eldorado
Olavarría
Venado Tuerto
Tartagal
Rio Grande
San Francisco
Concepción
Argentina (ARG) = ± s min = City population, log s C i t y G D P , l o g y Buenos Aires
Cordoba
Rosario
Mendoza
San Miguel de Tucumán
La Plata
Mar del Plata
Salta
San Juan
Santa Fe
Santiago del Estero
Resistencia
Neuquén
Corrientes
Posadas
San Salvador de Jujuy
Bahía Blanca
Paraná
Formosa
San Fernando del Valle de Catamarca
Comodoro Rivadavia
San Luis
La Rioja
Zárate
San Rafael
San Nicolás de los Arroyos
Concordia
Río Cuarto
San Martín
Tandil
Villa Mercedes
San Carlos de Bariloche
Reconquista
Río Gallegos
Santa Rosa
Luján
Presidencia Roque Sáenz Peña
General Roca
Trelew
Villa María
Villa Carlos Paz
Puerto Madryn
Rafaela
San Ramón de la Nueva Orán
Oberá
Goya
Pergamino
Junín
Gualeguaychu
Necochea
Viedma
Eldorado
Olavarría
Venado Tuerto
Tartagal
Rio Grande
San Francisco
Concepción
Argentina (ARG) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Australia (AUS) = ± s min = City population, log s C i t y r an k , l o g r Melbourne
Sydney
Brisbane
Perth
Adelaide
Gold Coast
Newcastle
Wollongong
Geelong
Maroochydore
Campbelltown
Woden
Hobart
Belconnen
Aitkenvale
Cairns
Toowoomba
Rockingham
Australia (AUS) = ± s min = City population, log s C i t y G D P , l o g y Melbourne
Sydney
Brisbane
Perth
Adelaide
Gold Coast
Newcastle
Wollongong
Geelong
Maroochydore
Campbelltown
Woden
Hobart
Belconnen
Aitkenvale
Cairns
Toowoomba
Rockingham
Australia (AUS) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Azerbaijan (AZE) = ± s min = City population, log s C i t y r an k , l o g r Baku
Ganja
Lankaran
Mingachevir
Nakhchivan irvan
C lilabad
Sheki
Masall
Barda
Sabirabad
Kurdamir
Shamakhi
Azerbaijan (AZE) = ± s min = City population, log s C i t y G D P , l o g y Baku
Ganja
Lankaran
Mingachevir
Nakhchivan irvan
C lilabad
Sheki
Masall
Barda
Sabirabad
Kurdamir
Shamakhi
Azerbaijan (AZE) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Burundi (BDI) = ± s min = City population, log s C i t y r an k , l o g r Bujumbura
Gitega
Ngozi
Muyinga
Kayanza
Rumonge
Kirundo
Makamba
Kayogoro
Nyanza Lac
Burundi (BDI) = ± s min = City population, log s C i t y G D P , l o g y Bujumbura
Gitega
Ngozi
Muyinga
Kayanza
Rumonge
Kirundo
Makamba
Kayogoro
Nyanza Lac
Burundi (BDI) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Belgium (BEL) = ± s min = City population, log s C i t y r an k , l o g r Brussels
Antwerp
Liège
Charleroi
Ghent
Kortrijk
Mons
Leuven
Bruges
Belgium (BEL) = ± s min = City population, log s C i t y G D P , l o g y Brussels
Antwerp
Liège
Charleroi
Ghent
Kortrijk
Mons
Leuven
Bruges
Belgium (BEL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Benin (BEN) = ± s min = City population, log s C i t y r an k , l o g r Cotonou
Porto-Novo
Parakou
Bohicon
Djougou
Kandi
Whydah
Malanville
Natitingou
Pobè
Kétou
Nikki
Lokossa
Banikoara
Tanguieta
Savalou
Allada
Tindji
Dassa-Zoumé
Benin (BEN) = ± s min = City population, log s C i t y G D P , l o g y Cotonou
Porto-Novo
Parakou
Bohicon
Djougou
Kandi
Whydah
Malanville
Natitingou
Pobè
Kétou
Nikki
Lokossa
Banikoara
Tanguieta
Savalou
Allada
Tindji
Dassa-Zoumé
Benin (BEN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Burkina Faso (BFA) = ± s min = City population, log s C i t y r an k , l o g r Ouagadougou
Bobo-Dioulasso
Fada N'Gourma
Koudougou
Ouahigouya
Kaya
Tenkodogo
Banfora
Dori
Dédougou
Houndé
Pouytenga
Bogandé
Gourcy
Sidéradougou
Bitou
Yako
Manni
Djibo
Nouna
Koupéla
Niangoloko
Tougan
Kongoussi
Leo
Ziniaré
Solenzo
Gaoua
Kombissiri
Boulsa
Burkina Faso (BFA) = ± s min = City population, log s C i t y G D P , l o g y Ouagadougou
Bobo-Dioulasso
Fada N'Gourma
Koudougou
Ouahigouya
Kaya
Tenkodogo
Banfora
Dori
Dédougou
Houndé
Pouytenga
Bogandé
Gourcy
Sidéradougou
Bitou
Yako
Manni
Djibo
Nouna
Koupéla
Niangoloko
Tougan
Kongoussi
Leo
Ziniaré
Solenzo
Gaoua
Kombissiri
Boulsa
Burkina Faso (BFA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Bangladesh (BGD) = ± s min = City population, log s C i t y r an k , l o g r Dhaka
Comilla
Chattogram
Dhaka
Sirajganj
Brahmanbaria
Bogura
Dhaka
Dhaka
Tangail
Khulna
Sylhet
Lakshmipur
Mymensingh
Rajshahi
Bangladesh (BGD) = ± s min = City population, log s C i t y G D P , l o g y Dhaka
Comilla
Chattogram
Dhaka
Sirajganj
Brahmanbaria
Bogura
Dhaka
Dhaka
Tangail
Khulna
Sylhet
Lakshmipur
Mymensingh
Rajshahi
Bangladesh (BGD) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Belarus (BLR) = ± s min = City population, log s C i t y r an k , l o g r Minsk
Homel
Vitebsk
Mahilyow
Hrodna
Brest
Babruysk
Baranovichi
Pinsk
Barysaw
Orsha
Zhodzina
Belarus (BLR) = ± s min = City population, log s C i t y G D P , l o g y Minsk
Homel
Vitebsk
Mahilyow
Hrodna
Brest
Babruysk
Baranovichi
Pinsk
Barysaw
Orsha
Zhodzina
Belarus (BLR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Bolivia (BOL) = ± s min = City population, log s C i t y r an k , l o g r El Alto [La Paz]
Santa Cruz de la Sierra
Cochabamba
Oruro
Sucre
Tarija
Potosí
Montero
Trinidad
Riberalta
Bolivia (BOL) = ± s min = City population, log s C i t y G D P , l o g y El Alto [La Paz]
Santa Cruz de la Sierra
Cochabamba
Oruro
Sucre
Tarija
Potosí
Montero
Trinidad
Riberalta
Bolivia (BOL) = ± .0 5.5 6.0 6.5 7.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Brazil (BRA) = ± s min = City population, log s C i t y r an k , l o g r São Paulo
Rio de Janeiro
Belo Horizonte
Recife
Fortaleza
Salvador
Curitiba
Porto Alegre
Campinas
Goiânia
Belém
Manaus
Sao Goncalo
Ceilândia
Santos
Vila Velha
São Luís
Natal
Maceió
João Pessoa
Teresina
Sao Jose dos Campos
Aracaju
Florianópolis
Sorocaba
Cuiabá
Campo Grande
Novo Hamburgo
Ribeirao Preto
Londrina
Uberlândia
Gama
Itajaí
Feira de Santana
Joinville
Macapá
Maringá
Juiz de Fora
Caxias do Sul
São José do Rio Preto
Taubaté
Volta Redonda
Ipatinga
Campina Grande
Blumenau
Petrolina
Porto Velho
Campos dos Goytacazes
Piracicaba
Juazeiro do Norte
Montes Claros
Rio Branco
Bauru
Anápolis
Franca
Ponta Grossa
Boa Vista
Pelotas
Criciúma
Caruaru
Limeira
Uberaba
Cascavel
Cabo Frio
Vitória da Conquista
Imperatriz
Mossoró
Santa Maria
Araraquara
Governador Valadares
Ciudad del Este
Guaratinguetá
São Carlos
Rio das Ostras
Presidente Prudente
Macaé
Divinópolis
Arapiraca
Marília
Indaiatuba
Sete Lagoas
Mogi Guaçu
Maraba
Santarém
Rio Claro
Rondonópolis
Parauapebas
Jaraguá do Sul
Itabuna
Camaçari
Chapecó
Dourados
Rio Verde
Águas Lindas de Goiás
Rio Grande
Cachoeiro de Itapemirim
Passo Fundo
Araçatuba
Castanhal
Planaltina
Palmas
Nova Friburgo
Sobradinho
Araguaína
Sobral
Teresópolis
Parnaíba
Araruama
Barreiras
Poços de Caldas
Lages
Guarapuava
Arapongas
Bragança Paulista
Teixeira de Freitas
Resende
Paranaguá
Bento Gonçalves
Pouso Alegre
Jequié
Alagoinhas
Ilhéus
Vitória de Santo Antão
Atibaia
Patos de Minas
Botucatu
Angra dos Reis
Itapetininga
Jaú
Varginha
Santa Cruz do Capibaribe
Catanduva
Sinop
Santa Cruz do Sul
Brazil (BRA) = ± s min = City population, log s C i t y G D P , l o g y São Paulo
Rio de Janeiro
Belo Horizonte
Recife
Fortaleza
Salvador
Curitiba
Porto Alegre
Campinas
Goiânia
Belém
Manaus
Sao Goncalo
Ceilândia
Santos
Vila Velha
São Luís
Natal
Maceió
João Pessoa
Teresina
Sao Jose dos Campos
Aracaju
Florianópolis
Sorocaba
Cuiabá
Campo Grande
Novo Hamburgo
Ribeirao Preto
Londrina
Uberlândia
Gama
Itajaí
Feira de Santana
Joinville
Macapá
Maringá
Juiz de Fora
Caxias do Sul
São José do Rio Preto
Taubaté
Volta Redonda
Ipatinga
Campina Grande
Blumenau
Petrolina
Porto Velho
Campos dos Goytacazes
Piracicaba
Juazeiro do Norte
Montes Claros
Rio Branco
Bauru
Anápolis
Franca
Ponta Grossa
Boa Vista
Pelotas
Criciúma
Caruaru
Limeira
Uberaba
Cascavel
Cabo Frio
Vitória da Conquista
Imperatriz
Mossoró
Santa Maria
Araraquara
Governador Valadares
Ciudad del Este
Guaratinguetá
São Carlos
Rio das Ostras
Presidente Prudente
Macaé
Divinópolis
Arapiraca
Marília
Indaiatuba
Sete Lagoas
Mogi Guaçu
Maraba
Santarém
Rio Claro
Rondonópolis
Parauapebas
Jaraguá do Sul
Itabuna
Camaçari
Chapecó
Dourados
Rio Verde
Águas Lindas de Goiás
Rio Grande
Cachoeiro de Itapemirim
Passo Fundo
Araçatuba
Castanhal
Planaltina
Palmas
Nova Friburgo
Sobradinho
Araguaína
Sobral
Teresópolis
Parnaíba
Araruama
Barreiras
Poços de Caldas
Lages
Guarapuava
Arapongas
Bragança Paulista
Teixeira de Freitas
Resende
Paranaguá
Bento Gonçalves
Pouso Alegre
Jequié
Alagoinhas
Ilhéus
Vitória de Santo Antão
Atibaia
Patos de Minas
Botucatu
Angra dos Reis
Itapetininga
Jaú
Varginha
Santa Cruz do Capibaribe
Catanduva
Sinop
Santa Cruz do Sul
Brazil (BRA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Canada (CAN) = ± s min = City population, log s C i t y r an k , l o g r Toronto
Montreal
Vancouver
Calgary
Ottawa
Edmonton
Quebec
Winnipeg
Kitchener
London
Halifax
Victoria
Detroit
St. Catharines
Saskatoon
Barrie
Regina
Sherbrooke
St. John's
Abbotsford
Trois-Rivières
Guelph
Saint-Jérôme
Saint-Jean-sur-Richelieu
Moncton
Kingston
Red Deer
Brantford
Nanaimo
Peterborough
Thunder Bay
Canada (CAN) = ± s min = City population, log s C i t y G D P , l o g y Toronto
Montreal
Vancouver
Calgary
Ottawa
Edmonton
Quebec
Winnipeg
Kitchener
London
Halifax
Victoria
Detroit
St. Catharines
Saskatoon
Barrie
Regina
Sherbrooke
St. John's
Abbotsford
Trois-Rivières
Guelph
Saint-Jérôme
Saint-Jean-sur-Richelieu
Moncton
Kingston
Red Deer
Brantford
Nanaimo
Peterborough
Thunder Bay
Canada (CAN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Switzerland (CHE) = ± s min = City population, log s C i t y r an k , l o g r Zurich
Geneva
Basel
Bern
Lausanne
Lucerne
Sankt Gallen
Olten
Lugano
Biel/Bienne
Montreux
Thun
Switzerland (CHE) = ± s min = City population, log s C i t y G D P , l o g y Zurich
Geneva
Basel
Bern
Lausanne
Lucerne
Sankt Gallen
Olten
Lugano
Biel/Bienne
Montreux
Thun
Switzerland (CHE) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Chile (CHL) = ± s min = City population, log s C i t y r an k , l o g r Santiago
Viña del Mar [Valparaíso]
Concepción
La Serena
Temuco
Rancagua
Talca
Iquique
Puerto Montt
Antofagasta
Chillán
Curicó
Chile (CHL) = ± s min = City population, log s C i t y G D P , l o g y Santiago
Viña del Mar [Valparaíso]
Concepción
La Serena
Temuco
Rancagua
Talca
Iquique
Puerto Montt
Antofagasta
Chillán
Curicó
Chile (CHL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) China (CHN) = ± s min = City population, log s C i t y r an k , l o g r Shanghai
Beijing
Guangzhou
Jieyang
Chengdu
Suzhou
Hangzhou
Guangzhou
Wuhan
Tianjin
Nanjing
Guangzhou
Xi'an
Quanzhou
Shenyang
Chongqing
Zhengzhou
Wenzhou
Xiamen
Qingdao
Hefei
Harbin
Guangzhou
Jinan
Shijiazhuang
Fuzhou
Nanchang
Changsha
Changchun
Taiyuan
Ningbo
Zibo
Dalian
Kunming
Guangzhou
Changzhou
Ürümqi
Guiyang
Cixi
Taizhou
Nanning
Lanzhou
Jiaxing
Xuzhou
Linyi
Luoyang
Tangshan
Baotou
Nantong
Hohhot
Guangzhou
Huizhou
Yantai
Xinxiang
Binhai
Haikou
Guangzhou
Anshan
Weifang
Liuzhou
Datong
Yiwu
Yinchuan
Handan
Baoding
Jilin
Zhuhai
Yangzhou
Tianjiaan
Huai'an
Anyang
Putian
Zhangjiagang
Fushun
Xining
Jiaozuo
Huangshi
Fancheng
Guangzhou
Zhongshan
Hengyang
Yueqing
Wuhu
Guilin
Yulin
Nanyang
Jiangyin
Xiangtan
Huaibei
Zhanjiang
Bengbu
Luohe
Zhuzhou
Baoji
Yancheng
Jinzhou
Shangqiu
Taizhou
Mianyang
Xingtai
Fuyang
Yongkang
Zunyi
Huangdao
Qinhuangdao
Changshu
Maoming
Jining
Xuchang
Yichang
Pingdingshan
Ganzhou
Tai'an
Shaoyang
Pingxiang
Yueyang
Kaifeng
Qiqihar
Puyang
Jingzhou
Changde
Zhenjiang
Benxi
Luzhou
Tengzhou
Ma'anshan
Nanchong
Cangzhou
Jiujiang
Lianyungang
Zhangzhou
Fuxin
Mudanjiang
Heze
Panjin
Jinhua
Gongyi
Qingyuan
Linfen
Changzhi
Wanzhou
Zhaoqing
Dezhou
Jiamusi
Langfang
Yangquan
Liaocheng
Shaoguan
Bayuquan
Zhangjiakou
Dandong
Chifeng
Ezhou
Liaoyang
Rizhao
Yixing
Yongnian
Laiyang
Anqing
Shiyan
Yibin
Zoucheng
Weihai
Huzhou
Beihai
Zigong
Yuzhou
Hanzhong
Zhoukou
Laiwu
Xingping
Suqian
Taixing
Xiangcheng
Zhuji
Yiyang
Xiaogan
Pukou
Tongliao
Fuzhou
Yangjiang
Xinmi
Panzhihua
Zucheng
Tianshui
Qingzhou
Tongling
Songyuan
Meizhou
Wenshui
Kashgar
Hegang
Kaiping
Jincheng
Yangzhong
Qujing
Jixi
Yingkou
Shengzhou
Lu'an
Zhumadian
Deyang
Xinyu
Haicheng
Siping
Suzhou
Dazhou
Shangrao
Yuhuan
Quzhou
Zhoushan
Lixian
Huludao
Ankang
Xitao
Beibei
Danyang
Zhangqiu
Shuyang
Xinyang
Xintai
Yanji
Neijiang
Jinzhong
Fuyang
Shouguang
Chaoyang
Daqing
Dujiangyan
Huaihua
Xinxing
Yichun
Xiantao
Wuzhou
Sanya
Tonghua
Linqu
Dongsheng
Sanmenxia
Haiyan
Fuqing
Liaoyuan
Gaomi
Longyan
Xingning
Pizhou
Zhaotong
Jingdezhen
Leshan
HengshuiYuxi
Binzhou
Chenzhou
Wuzhong
Liupanshui
Liyang
Yongchuan
Yuncheng
Xianyou
Gaobeidian
SuiningYining/Qulja
Meishan
Jingmen
Baoshan
Guigang
Changji/Sanji
Weinan
XinzhengShihezi
Yongcheng
Dali
Linying
Linhai
JintanDingzhou
Xiaoxiang
Leiyang
XinhuaDashiqiao
Suizhou
Jiangjin
ChuzhouShanwei
Heyuan
Ranghulu
Louxing
Renqiu
Ji'an
Tianshan
HechuanHuaxian
Conghua
Anshun
SuiningJiyuan
Xichang
Xuanhua
DengzhouGucheng
Wuwei
Juxian
HangyuluBozhou
FengfengPujiang
Pingdu
Tieling
YingtanHaian
Fengrun
ShanxianLinqing
Changxing
Qidong
Changge
Shuozhou
WuchuanLeping
Guangfeng
Shangcai
Tanghe
Rugao
JianhuWu'an
CaoxianChaohu
Lufeng
ShanchengZhuozhou
Leizhou
Shuangyashan
ChangyuanHuairou
HaimenBayannur
Xinjin
NinghaiPinghu
Longkou
HuaiyangLianjiang
LuchengUlanqab
Dongtai
Baoying
LilingLaizhou
Lanxi
Siyang
GaozhouPinggu
AksuXingyi
Wafangdian
HebiTaishan
XianningXushui
QinzhouHouma
Lishui
XinzhouWendeng
JiangyouZhaodong
KailiBinhai
NingxiangKaiyuan
Chengde
XinyiBaicheng
NanxunZiyang
LinxiaNankang
XinghuaCenxi
Hongtong
XuanchengFuning
HainingGushi
Donghai
YizhenBaishan
GanyuRuzhou
HuyiMancheng
Linquan
Binyang
MeihekouMiyun
XuanweiAcheng
Lüliang
Xinji
FenghuaLingshan
TaiheSanming
JurongBotou
SuihuaTianmenXiangyin
HezhouLuoding
FengxianDayi
EnshiXiaoyi
Lin'anPingliang
GaoanBijie
QingtianHotan
RuijinHanchuan
NingdeYangguHuangshan
YutianGaoping
SihongWuhua
KaramayYunfu
JianyangJiuquanZhenping
ChangshouGaoyou
LingbaoQidong
LuanzhouYunmeng
LhasaZhangyeYongzhou
QingheBobai
Yintai
PingtanWeiGuang'an
HamiAnji
DangshanLianshui
QijiangHulunbuirUlan Hot
AnningBazhou
PingyaoWuxueZhongmu
Qian'anGuanyun
QingyangLishuiQionglai
Zunhua
HuangchuanXinqiao
LuchengFengshunJiexiu
Lili
GuipingSheyangYushan
WenshanAnxiJinghai
Enping
BazhongNanpingAnda
XinshiHejian
Ya'anDanzhou
ChipingJishou
ShaodongXinyi
WeishiLinzhouTang
HuazhouZhangjiajie
NingjinShulan
MachengGuannan
SanchaheJizhouJiangshan
GaochunDianjiangDunhua
BaiyinZhao
DuyunCi
XiangxiangBoxingShenxian
LaolingQuxian
GongzhulingYiyuanFula'erji
RushanFenyangMengzhou
Zaoyang
LiuyangXiangshanJiayuguan
PoyangJuanchengShuangcheng
YimaYichuan
ZhechengRudong
DafengYushuChibi
YangchunJieshiTongliang
TongluLingyuanShenmu
HuangpiRongchangJinzhou
FeixianLixinAnlu
DongpingChangliRenshou
YuganDaladRunanXuwen County
FushunMengziYan'an
YunyangXingchengHuarong
LvsigangFu'anLiangmatai
ZhongxiangJuyeLangzhong
FunanLantianBaode
ShengfangZhongwei
XipingSanheQianjiang
QixianSui
JieshouXinleShucheng
NanbuJianshui
WujiGejiuXianghe
HuairenYingchengPulandianJinxian
WenshangGuantao
ChizhouSongziNanxian
RongchengKaizhouTiantai
JiaziHanchengYingdeYongchun
YongjiChangqi
DazhuXinfengGuoyangTongchuan
XinzhouLongchangFangcheng
XincaiEmeishanLushanGu'an
NingguoLongchuanLaibin
YanlingWugangChongmingYingshan
DangyangLijiangMianxianTaikang
GanguQionghaiFuding
ShifangZijinTangyinLianjiang
ShayuanYong'anLianyuan
XingguoDehuaZhaoyuan
YuanjiangYunyangTongren
NingduDehuiLongshanNeihuang
Pu'erQianxiYuchengYangling
DengfengLujiangMengcheng
Hong'anShizuishanDanjiangkouXinxing
BiyangZhuangheDanchengLingling
ShangluoKuqaYiyangAnping
BaidiDengfengGaochengYanqing
XinminLongxiShaxiXilinhot
TaojiangWulianGongnongLiulin
JinxiangHengyangGuangshuiYuanyang
YichengZhongQiyangDiaobingshan
RongxianXianJuGaoyiDonggang
JinchangWuheYuanpingTongcheng
JiaWenNanchuanLinShui
Gong'anZhangshuDong'eDongxian
YunxiaoJintangFengcheng
DingyuanYuLuyiDeqing
WuchangXuyiLintaoJingbianHengxian
JiulongbaXiayi
ZhijiangHeishanShangliFengqiu
LuannanWangchengTianchangJiawangPucheng
JnchéngjingLingbiCaijiapoJiutai
HuaijiWuyangBeipiaoLiuzhiQuyang
FengduQinyangSheLaoting
XiaochangHunchunQingHuozhou
China (CHN) = ± s min = City population, log s C i t y G D P , l o g y Shanghai
Beijing
Guangzhou
Jieyang
Chengdu
Suzhou
Hangzhou
Guangzhou
Wuhan
Tianjin
Nanjing
Guangzhou
Xi'an
Quanzhou
Shenyang
Chongqing
Zhengzhou
Wenzhou
Xiamen
Qingdao
Hefei
Harbin
Guangzhou
Jinan
Shijiazhuang
Fuzhou
Nanchang
Changsha
Changchun
Taiyuan
Ningbo
Zibo
Dalian
Kunming
Guangzhou
Changzhou
Ürümqi
Guiyang
Cixi
Taizhou
Nanning
Lanzhou
Jiaxing
Xuzhou
Linyi
Luoyang
Tangshan
Baotou
Nantong
Hohhot
Guangzhou
Huizhou
Yantai
Xinxiang
Binhai
Haikou
Guangzhou
Anshan
Weifang
Liuzhou
Datong
Yiwu
Yinchuan
Handan
Baoding
Jilin
Zhuhai
Yangzhou
Tianjiaan
Huai'an
Anyang
Putian
Zhangjiagang
Fushun
Xining
Jiaozuo
Huangshi
Fancheng
Guangzhou
Zhongshan
Hengyang
Yueqing
Wuhu
Guilin
Yulin
Nanyang
Jiangyin
Xiangtan
Huaibei
Zhanjiang
Bengbu
Luohe
Zhuzhou
Baoji
Yancheng
Jinzhou
Shangqiu
Taizhou
Mianyang
Xingtai
Fuyang
Yongkang
Zunyi
Huangdao
Qinhuangdao
Changshu
Maoming
Jining
Xuchang
Yichang
Pingdingshan
Ganzhou
Tai'an
Shaoyang
Pingxiang
Yueyang
Kaifeng
Qiqihar
Puyang
Jingzhou
Changde
Zhenjiang
Benxi
Luzhou
Tengzhou
Ma'anshan
Nanchong
Cangzhou
Jiujiang
Lianyungang
Zhangzhou
Fuxin
Mudanjiang
Heze
Panjin
Jinhua
Gongyi
Qingyuan
Linfen
Changzhi
Wanzhou
Zhaoqing
Dezhou
Jiamusi
Langfang
Yangquan
Liaocheng
Shaoguan
Bayuquan
Zhangjiakou
Dandong
Chifeng
Ezhou
Liaoyang
Rizhao
Yixing
Yongnian
Laiyang
Anqing
Shiyan
Yibin
Zoucheng
Weihai
Huzhou
Beihai
Zigong
Yuzhou
Hanzhong
Zhoukou
Laiwu
Xingping
Suqian
Taixing
Xiangcheng
Zhuji
Yiyang
Xiaogan
Pukou
Tongliao
Fuzhou
Yangjiang
Xinmi
Panzhihua
Zucheng
Tianshui
Qingzhou
Tongling
Songyuan
Meizhou
Wenshui
Kashgar
Hegang
Kaiping
Jincheng
Yangzhong
Qujing
Jixi
Yingkou
Shengzhou
Lu'an
Zhumadian
Deyang
Xinyu
Haicheng
Siping
Suzhou
Dazhou
Shangrao
Yuhuan
Quzhou
Zhoushan
Lixian
Huludao
Ankang
Xitao
Beibei
Danyang
Zhangqiu
Shuyang
Xinyang
Xintai
Yanji
Neijiang
Jinzhong
Fuyang
Shouguang
Chaoyang
Daqing
Dujiangyan
Huaihua
Xinxing
Yichun
Xiantao
Wuzhou
Sanya
Tonghua
Linqu
Dongsheng
Sanmenxia
Haiyan
Fuqing
Liaoyuan
Gaomi
Longyan
Xingning
Pizhou
Zhaotong
Jingdezhen
Leshan
HengshuiYuxi
Binzhou
Chenzhou
Wuzhong
Liupanshui
Liyang
Yongchuan
Yuncheng
Xianyou
Gaobeidian
SuiningYining/Qulja
Meishan
Jingmen
Baoshan
Guigang
Changji/Sanji
Weinan
XinzhengShihezi
Yongcheng
Dali
Linying
Linhai
JintanDingzhou
Xiaoxiang
Leiyang
XinhuaDashiqiao
Suizhou
Jiangjin
ChuzhouShanwei
Heyuan
Ranghulu
Louxing
Renqiu
Ji'an
Tianshan
HechuanHuaxian
Conghua
Anshun
SuiningJiyuan
Xichang
Xuanhua
DengzhouGucheng
Wuwei
Juxian
HangyuluBozhou
FengfengPujiang
Pingdu
Tieling
YingtanHaian
Fengrun
ShanxianLinqing
Changxing
Qidong
Changge
Shuozhou
WuchuanLeping
Guangfeng
Shangcai
Tanghe
Rugao
JianhuWu'an
CaoxianChaohu
Lufeng
ShanchengZhuozhou
Leizhou
Shuangyashan
ChangyuanHuairou
HaimenBayannur
Xinjin
NinghaiPinghu
Longkou
HuaiyangLianjiang
LuchengUlanqab
Dongtai
Baoying
LilingLaizhou
Lanxi
Siyang
GaozhouPinggu
AksuXingyi
Wafangdian
HebiTaishan
XianningXushui
QinzhouHouma
Lishui
XinzhouWendeng
JiangyouZhaodong
KailiBinhai
NingxiangKaiyuan
Chengde
XinyiBaicheng
NanxunZiyang
LinxiaNankang
XinghuaCenxi
Hongtong
XuanchengFuning
HainingGushi
Donghai
YizhenBaishan
GanyuRuzhou
HuyiMancheng
Linquan
Binyang
MeihekouMiyun
XuanweiAcheng
Lüliang
Xinji
FenghuaLingshan
TaiheSanming
JurongBotou
SuihuaTianmenXiangyin
HezhouLuoding
FengxianDayi
EnshiXiaoyi
Lin'anPingliang
GaoanBijie
QingtianHotan
RuijinHanchuan
NingdeYangguHuangshan
YutianGaoping
SihongWuhua
KaramayYunfu
JianyangJiuquanZhenping
ChangshouGaoyou
LingbaoQidong
LuanzhouYunmeng
LhasaZhangyeYongzhou
QingheBobai
Yintai
PingtanWeiGuang'an
HamiAnji
DangshanLianshui
QijiangHulunbuirUlan Hot
AnningBazhou
PingyaoWuxueZhongmu
Qian'anGuanyun
QingyangLishuiQionglai
Zunhua
HuangchuanXinqiao
LuchengFengshunJiexiu
Lili
GuipingSheyangYushan
WenshanAnxiJinghai
Enping
BazhongNanpingAnda
XinshiHejian
Ya'anDanzhou
ChipingJishou
ShaodongXinyi
WeishiLinzhouTang
HuazhouZhangjiajie
NingjinShulan
MachengGuannan
SanchaheJizhouJiangshan
GaochunDianjiangDunhua
BaiyinZhao
DuyunCi
XiangxiangBoxingShenxian
LaolingQuxian
GongzhulingYiyuanFula'erji
RushanFenyangMengzhou
Zaoyang
LiuyangXiangshanJiayuguan
PoyangJuanchengShuangcheng
YimaYichuan
ZhechengRudong
DafengYushuChibi
YangchunJieshiTongliang
TongluLingyuanShenmu
HuangpiRongchangJinzhou
FeixianLixinAnlu
DongpingChangliRenshou
YuganDaladRunanXuwen County
FushunMengziYan'an
YunyangXingchengHuarong
LvsigangFu'anLiangmatai
ZhongxiangJuyeLangzhong
FunanLantianBaode
ShengfangZhongwei
XipingSanheQianjiang
QixianSui
JieshouXinleShucheng
NanbuJianshui
WujiGejiuXianghe
HuairenYingchengPulandianJinxian
WenshangGuantao
ChizhouSongziNanxian
RongchengKaizhouTiantai
JiaziHanchengYingdeYongchun
YongjiChangqi
DazhuXinfengGuoyangTongchuan
XinzhouLongchangFangcheng
XincaiEmeishanLushanGu'an
NingguoLongchuanLaibin
YanlingWugangChongmingYingshan
DangyangLijiangMianxianTaikang
GanguQionghaiFuding
ShifangZijinTangyinLianjiang
ShayuanYong'anLianyuan
XingguoDehuaZhaoyuan
YuanjiangYunyangTongren
NingduDehuiLongshanNeihuang
Pu'erQianxiYuchengYangling
DengfengLujiangMengcheng
Hong'anShizuishanDanjiangkouXinxing
BiyangZhuangheDanchengLingling
ShangluoKuqaYiyangAnping
BaidiDengfengGaochengYanqing
XinminLongxiShaxiXilinhot
TaojiangWulianGongnongLiulin
JinxiangHengyangGuangshuiYuanyang
YichengZhongQiyangDiaobingshan
RongxianXianJuGaoyiDonggang
JinchangWuheYuanpingTongcheng
JiaWenNanchuanLinShui
Gong'anZhangshuDong'eDongxian
YunxiaoJintangFengcheng
DingyuanYuLuyiDeqing
WuchangXuyiLintaoJingbianHengxian
JiulongbaXiayi
ZhijiangHeishanShangliFengqiu
LuannanWangchengTianchangJiawangPucheng
JnchéngjingLingbiCaijiapoJiutai
HuaijiWuyangBeipiaoLiuzhiQuyang
FengduQinyangSheLaoting
XiaochangHunchunQingHuozhou
China (CHN) = ± .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Cote d Ivoire (CIV) = ± s min = City population, log s C i t y r an k , l o g r Abidjan
Bouaké
Daloa
Korhogo
Yamoussoukro
San-Pédro
Gagnoa
Man
Divo
Bouaflé
Duekoue
Soubré
Abengourou
Sinfra
Méagui
Ferkéssédougou
Cote d Ivoire (CIV) = ± s min = City population, log s C i t y G D P , l o g y Abidjan
Bouaké
Daloa
Korhogo
Yamoussoukro
San-Pédro
Gagnoa
Man
Divo
Bouaflé
Duekoue
Soubré
Abengourou
Sinfra
Méagui
Ferkéssédougou
Cote d Ivoire (CIV) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Cameroon (CMR) = ± s min = City population, log s C i t y r an k , l o g r Yaounde
Douala
Garoua
Maroua
Mokolo
Bamenda
N'Djamena
Bafoussam
Ngaoundéré
Guider
Yagoua
Kaele
Kumba
Bertoua
Kribi
Ebolowa
Mora
Mbouda
Tiko
Kumbo
Limbé
Foumban
Banyo
Foumbot
Tcholliré
Wum
Meiganga
Ndop
Batouri
Gamboru
Mbalmayo
Banki
Edéa
Ngaoundal
Bafia
Dschang
Nkongsamba
Mamfe
Cameroon (CMR) = ± s min = City population, log s C i t y G D P , l o g y Yaounde
Douala
Garoua
Maroua
Mokolo
Bamenda
N'Djamena
Bafoussam
Ngaoundéré
Guider
Yagoua
Kaele
Kumba
Bertoua
Kribi
Ebolowa
Mora
Mbouda
Tiko
Kumbo
Limbé
Foumban
Banyo
Foumbot
Tcholliré
Wum
Meiganga
Ndop
Batouri
Gamboru
Mbalmayo
Banki
Edéa
Ngaoundal
Bafia
Dschang
Nkongsamba
Mamfe
Cameroon (CMR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Democratic Republicof the Congo (COD) = ± s min = City population, log s C i t y r an k , l o g r Kinshasa
Mbuji-Mayi
Lubumbashi
Beni
Kananga
Bukavu
Kisangani
Goma
Bunia
Mahagi
Tshikapa
Mongbwalu
Kikwit
Kalemie
Uvira
Likasi
Kamina
Butembo
Mbandaka
Gemena
Manono
Rubaya
Kilwa
Ariwara
Butondo
Kolwezi
Kongolo
Bumba
Mwene-Ditu
Kindu
Boma
Kambove
Kabinda
Aru
Baraka
Sake
Buta
Lisala
Basankusu
Bandundu
Kipushi
Malemba Nkulu
Mukubu
Mulongo
Demba
Kasumbalesa
Iga Barriere
Elila
Matadi
Isiro
Kenge
Kasaji
Tshela
Kamituga
Kabondo-Dianda
Kamanyola
Punia
Kinzao
Butusande
Dungu
Lubao
Democratic Republicof the Congo (COD) = ± s min = City population, log s C i t y G D P , l o g y Kinshasa
Mbuji-Mayi
Lubumbashi
Beni
Kananga
Bukavu
Kisangani
Goma
Bunia
Mahagi
Tshikapa
Mongbwalu
Kikwit
Kalemie
Uvira
Likasi
Kamina
Butembo
Mbandaka
Gemena
Manono
Rubaya
Kilwa
Ariwara
Butondo
Kolwezi
Kongolo
Bumba
Mwene-Ditu
Kindu
Boma
Kambove
Kabinda
Aru
Baraka
Sake
Buta
Lisala
Basankusu
Bandundu
Kipushi
Malemba Nkulu
Mukubu
Mulongo
Demba
Kasumbalesa
Iga Barriere
Elila
Matadi
Isiro
Kenge
Kasaji
Tshela
Kamituga
Kabondo-Dianda
Kamanyola
Punia
Kinzao
Butusande
Dungu
Lubao
Democratic Republicof the Congo (COD) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Colombia (COL) = ± s min = City population, log s C i t y r an k , l o g r Bogota
Medellín
Cali
Barranquilla
Bucaramanga
Cartagena
Cúcuta
Pereira
Ibagué
Santa Marta
Manizales
Villavicencio
Pasto
Montería
Valledupar
El esfuerzo
Neiva
Popayán
Armenia
Sincelejo
Riohacha
Palmira
Sahagún
Tuluá
Barrancabermeja
Tunja
Yopal
Florencia
Maicao
Rionegro
Jamundí
Facatativá
Girardot
Quibdó
Zipaquirá
Cartago
Tumaco
Fusagasugá
Piedecuesta
Apartadó
Ciénaga
Ipiales
Pitalito
Duitama
Buga
Manaure
Uribia
Sogamoso
Tierralta
Caucasia
Ocaña
Magangué
Aguachica
Lorica
Garzón
La Dorada
Montelíbano
Santander de Quilichao
Tiquisio
Arauca
San Vicente del Caguán
Sabanalarga
San José del Guaviare
Cereté
Espinal
San Andrés
Fundación
Santa Rosa de Cabal
Calarcá
Morroa
Chiquinquirá
Manuela
Chigorodó
Turbaco
Puerto Asís
Arjona
Puerto Boyacá
Planeta Rica
El Carmen de Bolívar
Orito
Colombia (COL) = ± s min = City population, log s C i t y G D P , l o g y Bogota
Medellín
Cali
Barranquilla
Bucaramanga
Cartagena
Cúcuta
Pereira
Ibagué
Santa Marta
Manizales
Villavicencio
Pasto
Montería
Valledupar
El esfuerzo
Neiva
Popayán
Armenia
Sincelejo
Riohacha
Palmira
Sahagún
Tuluá
Barrancabermeja
Tunja
Yopal
Florencia
Maicao
Rionegro
Jamundí
Facatativá
Girardot
Quibdó
Zipaquirá
Cartago
Tumaco
Fusagasugá
Piedecuesta
Apartadó
Ciénaga
Ipiales
Pitalito
Duitama
Buga
Manaure
Uribia
Sogamoso
Tierralta
Caucasia
Ocaña
Magangué
Aguachica
Lorica
Garzón
La Dorada
Montelíbano
Santander de Quilichao
Tiquisio
Arauca
San Vicente del Caguán
Sabanalarga
San José del Guaviare
Cereté
Espinal
San Andrés
Fundación
Santa Rosa de Cabal
Calarcá
Morroa
Chiquinquirá
Manuela
Chigorodó
Turbaco
Puerto Asís
Arjona
Puerto Boyacá
Planeta Rica
El Carmen de Bolívar
Orito
Colombia (COL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Cuba (CUB) = ± s min = City population, log s C i t y r an k , l o g r Havana
Santiago de Cuba
Holguín
Camagüey
Santa Clara
Bayamo
Cuba (CUB) = ± s min = City population, log s C i t y G D P , l o g y Havana
Santiago de Cuba
Holguín
Camagüey
Santa Clara
Bayamo
Cuba (CUB) = ± .2 5.4 5.6 5.8 6.0 6.2 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Czech Republic (CZE) = ± s min = City population, log s C i t y r an k , l o g r Prague
Brno
Ostrava
Pilsen
Ústí nad Labem
Olomouc
Liberec
Havíov
Pardubice
Hradec Králové
Czech Republic (CZE) = ± s min = City population, log s C i t y G D P , l o g y Prague
Brno
Ostrava
Pilsen
Ústí nad Labem
Olomouc
Liberec
Havíov
Pardubice
Hradec Králové
Czech Republic (CZE) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Germany (DEU) = ± s min = City population, log s C i t y r an k , l o g r Dortmund
Berlin
Cologne
Frankfurt am Main
Hamburg
Munich
Stuttgart
Mannheim
Nuremberg
Hanover
Dusseldorf
Dresden
Bremen
Wuppertal
Karlsruhe
Bielefeld
Leipzig
Mönchengladbach
Saarbruecken
Augsburg
Heerlen
Brunswick
Koblenz
Chemnitz
Münster
Freiburg im Breisgau
Kassel
Kiel
Osnabrück
Darmstadt
Reutlingen
Magdeburg
Heilbronn
Lübeck
Halle (Saale)
Ulm
Regensburg
Gießen
Würzburg
Rostock
Aschaffenburg
Oldenburg
Erfurt
Germany (DEU) = ± s min = City population, log s C i t y G D P , l o g y Dortmund
Berlin
Cologne
Frankfurt am Main
Hamburg
Munich
Stuttgart
Mannheim
Nuremberg
Hanover
Dusseldorf
Dresden
Bremen
Wuppertal
Karlsruhe
Bielefeld
Leipzig
Mönchengladbach
Saarbruecken
Augsburg
Heerlen
Brunswick
Koblenz
Chemnitz
Münster
Freiburg im Breisgau
Kassel
Kiel
Osnabrück
Darmstadt
Reutlingen
Magdeburg
Heilbronn
Lübeck
Halle (Saale)
Ulm
Regensburg
Gießen
Würzburg
Rostock
Aschaffenburg
Oldenburg
Erfurt
Germany (DEU) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Dominican Republic (DOM) = ± s min = City population, log s C i t y r an k , l o g r Santo Domingo
Santiago de los Caballeros
La Romana
Higüey
San Pedro de Macorís
San Francisco de Macoris
La Vega
Puerto Plata
Moca
Bonao
Baní
Barahona
San Juan de la Maguana
Dominican Republic (DOM) = ± s min = City population, log s C i t y G D P , l o g y Santo Domingo
Santiago de los Caballeros
La Romana
Higüey
San Pedro de Macorís
San Francisco de Macoris
La Vega
Puerto Plata
Moca
Bonao
Baní
Barahona
San Juan de la Maguana
Dominican Republic (DOM) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Algeria (DZA) = ± s min = City population, log s C i t y r an k , l o g r Algiers
Oran
Constantine
Blida
Annaba
Djelfa
Setif
Ash Shalif
Batna
Tlemcen
Mostaganem
Skikda
Sidi Bel Abbes
El Oued
Biskra
Ouargla
Tebessa
Bordj Bou Arreridjj
Bejaia
Tiaret
Jijel
El Eulma
Souk Ahras
Bashar
M'Sila
Saida
Guelma
Laghouat
Medea
Relizane
Aflou
Touggourt
Ain Turk
Tizi Ouzou
Khenchela
Mascara
Bou Saada
Algeria (DZA) = ± s min = City population, log s C i t y G D P , l o g y Algiers
Oran
Constantine
Blida
Annaba
Djelfa
Setif
Ash Shalif
Batna
Tlemcen
Mostaganem
Skikda
Sidi Bel Abbes
El Oued
Biskra
Ouargla
Tebessa
Bordj Bou Arreridjj
Bejaia
Tiaret
Jijel
El Eulma
Souk Ahras
Bashar
M'Sila
Saida
Guelma
Laghouat
Medea
Relizane
Aflou
Touggourt
Ain Turk
Tizi Ouzou
Khenchela
Mascara
Bou Saada
Algeria (DZA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Ecuador (ECU) = ± s min = City population, log s C i t y r an k , l o g r Guayaquil
Quito
Cuenca
Ambato
Manta
Cantón Santo Domingo de los Tsachilas
Portoviejo
Machala
Santa Elena
Riobamba
Ibarra
City of Loja
Quevedo
Esmeraldas
Milagro
Ecuador (ECU) = ± s min = City population, log s C i t y G D P , l o g y Guayaquil
Quito
Cuenca
Ambato
Manta
Cantón Santo Domingo de los Tsachilas
Portoviejo
Machala
Santa Elena
Riobamba
Ibarra
City of Loja
Quevedo
Esmeraldas
Milagro
Ecuador (ECU) = ± .0 5.5 6.0 6.5 7.0 7.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Egypt (EGY) = ± s min = City population, log s C i t y r an k , l o g r Cairo
Mansoura
Alexandria
Asyut
Luxor
Sohag
Girga
Faiyum
An Nazlah
Tanta
Al-Minya
Al-Zaqaziq
El Mahalla El Kubra
Beni Suef
Banha
Al Ismailiya
Port Said
Al-Manzala
Damietta
Desouk
Suez
Mallawi
Damanhur
Samalut
Aswan
Kafr Al-Sheikh
Shimm al Basal al Bahari
Rosetta
Tala
Beni Mazar
Qena
Nazlet al Mughrebi
Fazarah bil Qaryah
Abu Tig
Marsa Matruh
Maghagheh
Abu Manna Gharb
Itay el-Barud
Isna
Abu Huminus
Faris
Kafr al Hawi
Idku
Fashn
Al Arish
Nazlet Abu Haseiba
Kafr Dinshawai
Zayyan
Ezbet Ahmad al Ballasi
Shamma
Kafr al Hajj Shirbini
Shubra Khit
Delingat
Qaryat Salah al Din
Sadat City
Ihnasya al Madinah
Ezbet al Sibil Qiblli
Hawsh Isa
Al Zayyatin al Qibliyah
Hurghada
Minshat al Maghaliqah
Geziret Nikla
Dayr Abu Maqrufah
Al Inab al Saghirah
Bilqas
Al Balakus
Nazlat Dahrut
Qotur
Atmeeda
Beni Adi
Mutubis
Egypt (EGY) = ± s min = City population, log s C i t y G D P , l o g y Cairo
Mansoura
Alexandria
Asyut
Luxor
Sohag
Girga
Faiyum
An Nazlah
Tanta
Al-Minya
Al-Zaqaziq
El Mahalla El Kubra
Beni Suef
Banha
Al Ismailiya
Port Said
Al-Manzala
Damietta
Desouk
Suez
Mallawi
Damanhur
Samalut
Aswan
Kafr Al-Sheikh
Shimm al Basal al Bahari
Rosetta
Tala
Beni Mazar
Qena
Nazlet al Mughrebi
Fazarah bil Qaryah
Abu Tig
Marsa Matruh
Maghagheh
Abu Manna Gharb
Itay el-Barud
Isna
Abu Huminus
Faris
Kafr al Hawi
Idku
Fashn
Al Arish
Nazlet Abu Haseiba
Kafr Dinshawai
Zayyan
Ezbet Ahmad al Ballasi
Shamma
Kafr al Hajj Shirbini
Shubra Khit
Delingat
Qaryat Salah al Din
Sadat City
Ihnasya al Madinah
Ezbet al Sibil Qiblli
Hawsh Isa
Al Zayyatin al Qibliyah
Hurghada
Minshat al Maghaliqah
Geziret Nikla
Dayr Abu Maqrufah
Al Inab al Saghirah
Bilqas
Al Balakus
Nazlat Dahrut
Qotur
Atmeeda
Beni Adi
Mutubis
Egypt (EGY) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Spain (ESP) = ± s min = City population, log s C i t y r an k , l o g r Madrid
Barcelona
Valencia
Seville
Málaga
Bilbao
Zaragoza
Murcia
Las Palmas de Gran Canaria
Palma de Mallorca
Alacant / Alicante
Granada
Vigo
Santa Cruz de Tenerife
Tarragona
Donostia / San Sebastián
A Coruña
Valladolid
Castellón de la Plana
Pamplona
Oviedo
Santander
Córdoba
Gijón
Elx / Elche
Cádiz
Jerez
Almeria
Vitoria-Gasteiz
Torrevieja
Spain (ESP) = ± s min = City population, log s C i t y G D P , l o g y Madrid
Barcelona
Valencia
Seville
Málaga
Bilbao
Zaragoza
Murcia
Las Palmas de Gran Canaria
Palma de Mallorca
Alacant / Alicante
Granada
Vigo
Santa Cruz de Tenerife
Tarragona
Donostia / San Sebastián
A Coruña
Valladolid
Castellón de la Plana
Pamplona
Oviedo
Santander
Córdoba
Gijón
Elx / Elche
Cádiz
Jerez
Almeria
Vitoria-Gasteiz
Torrevieja
Spain (ESP) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Ethiopia (ETH) = ± s min = City population, log s C i t y r an k , l o g r Addis Ababa
Bahir Dar
Adama
Dire Dawa
Shashamane
Hawassa
Dessie
Jijiga
Bishoftu
Quiha
Arsi Negelle
Alaba Kulito
Yirgalem
Gonder
Merawi / Bule Hora
Bonsa Bota
Kombolcha
Wereta
Chiro
Aletawendo
Jinka
Morocho
Mota
Kefole
Areka
Kobo
Harar
Debre Markos
Seka
Gundo Meskel
Asassa
Adet
Gut'O
Debre Birhan
Nekemte
Asella
Jimma
Debark
Chucko
Ebbenat
Nefas Meewcha
Dodolla
Ambo
Boditi
Meki
Kersa
Bila
Chagni
Digna
Shone
Gelemso
Adigrat
Bekoji
Dambidollo
Kebri Dehar
Arbe Gona
Karamile
Dangla
Robe
Fik'
Aykel
Debre Tabor
Gojo Town
Ethiopia (ETH) = ± s min = City population, log s C i t y G D P , l o g y Addis Ababa
Bahir Dar
Adama
Dire Dawa
Shashamane
Hawassa
Dessie
Jijiga
Bishoftu
Quiha
Arsi Negelle
Alaba Kulito
Yirgalem
Gonder
Merawi / Bule Hora
Bonsa Bota
Kombolcha
Wereta
Chiro
Aletawendo
Jinka
Morocho
Mota
Kefole
Areka
Kobo
Harar
Debre Markos
Seka
Gundo Meskel
Asassa
Adet
Gut'O
Debre Birhan
Nekemte
Asella
Jimma
Debark
Chucko
Ebbenat
Nefas Meewcha
Dodolla
Ambo
Boditi
Meki
Kersa
Bila
Chagni
Digna
Shone
Gelemso
Adigrat
Bekoji
Dambidollo
Kebri Dehar
Arbe Gona
Karamile
Dangla
Robe
Fik'
Aykel
Debre Tabor
Gojo Town
Ethiopia (ETH) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) France (FRA) = ± s min = City population, log s C i t y r an k , l o g r Paris
Lyon
Marseille
Toulouse
Nice
Lille
Bordeaux
Lens
Nantes
Strasbourg
Rouen
Montpellier
Toulon
Grenoble
Rennes
Mulhouse
Saint-Étienne
Tours
Avignon
Clermont-Ferrand
Nancy
Perpignan
Caen
Valenciennes
Orléans
Angers
Metz
Le Havre
Dijon
Brest
Le Mans
Nimes
Valence
Reims
France (FRA) = ± s min = City population, log s C i t y G D P , l o g y Paris
Lyon
Marseille
Toulouse
Nice
Lille
Bordeaux
Lens
Nantes
Strasbourg
Rouen
Montpellier
Toulon
Grenoble
Rennes
Mulhouse
Saint-Étienne
Tours
Avignon
Clermont-Ferrand
Nancy
Perpignan
Caen
Valenciennes
Orléans
Angers
Metz
Le Havre
Dijon
Brest
Le Mans
Nimes
Valence
Reims
France (FRA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) United Kingdom (GBR) = ± s min = City population, log s C i t y r an k , l o g r London
Manchester
Birmingham
Leeds
Glasgow
Newcastle upon Tyne
Liverpool
Nottingham
Portsmouth
Bristol
Sheffield
Cardiff
Belfast
Brighton
Leicester
Edinburgh
Bournemouth
Middlesbrough
Southend-on-Sea
Coventry
Blackwater
Stoke-on-Trent
Swansea
Hull
Gloucester
Oxford
Blackburn
Cambridge
Norwich
Reading
Peterborough
Swindon
Plymouth
Preston
Luton
Ipswich
Colchester
Milton Keynes
Chester
Corby
Aberdeen
Northampton
Dundee
Chelmsford
Larbert
Exeter
Blackpool
Lincoln
Bedford
York
United Kingdom (GBR) = ± s min = City population, log s C i t y G D P , l o g y London
Manchester
Birmingham
Leeds
Glasgow
Newcastle upon Tyne
Liverpool
Nottingham
Portsmouth
Bristol
Sheffield
Cardiff
Belfast
Brighton
Leicester
Edinburgh
Bournemouth
Middlesbrough
Southend-on-Sea
Coventry
Blackwater
Stoke-on-Trent
Swansea
Hull
Gloucester
Oxford
Blackburn
Cambridge
Norwich
Reading
Peterborough
Swindon
Plymouth
Preston
Luton
Ipswich
Colchester
Milton Keynes
Chester
Corby
Aberdeen
Northampton
Dundee
Chelmsford
Larbert
Exeter
Blackpool
Lincoln
Bedford
York
United Kingdom (GBR) = ± .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Ghana (GHA) = ± s min = City population, log s C i t y r an k , l o g r Accra
Kumasi
Takoradi [Sekondi-Takoradi]
Tamale
Cape Coast
Yendi
Koforidua Ho Bawku
Obuasi
Hohoe
Techiman
Sunyani
Agona Swedru
Somanya
Bolgatanga
Berekum
Savelugu
Garu
Gushiegu
Akim Oda
Kintampo
Bimbila
Navrongo
Walewale Wa Winneba
Asamankese
Dormaa Ahenkro
New Tafo Akim
Suhum
Nkawkaw
Atebubu
Akatsi
UNNAMED
Salaga
Assin Fosu
Nkoranza
Dambai
Konongo
Lomé
Karaga
Yeji
Nalerigu
Wenchi
Dunkwa-on-Ofin
Ghana (GHA) = ± s min = City population, log s C i t y G D P , l o g y Accra
Kumasi
Takoradi [Sekondi-Takoradi]
Tamale
Cape Coast
Yendi
Koforidua Ho Bawku
Obuasi
Hohoe
Techiman
Sunyani
Agona Swedru
Somanya
Bolgatanga
Berekum
Savelugu
Garu
Gushiegu
Akim Oda
Kintampo
Bimbila
Navrongo
Walewale Wa Winneba
Asamankese
Dormaa Ahenkro
New Tafo Akim
Suhum
Nkawkaw
Atebubu
Akatsi
UNNAMED
Salaga
Assin Fosu
Nkoranza
Dambai
Konongo
Lomé
Karaga
Yeji
Nalerigu
Wenchi
Dunkwa-on-Ofin
Ghana (GHA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Guinea (GIN) = ± s min = City population, log s C i t y r an k , l o g r Conakry
Kankan
Nzérékoré
Kindia
Siguiri
Labé
Kamsar
Kissidougou
Faranah
Mamou
Sangarédi
Sinko
Macenta
Guéckédou
Boké
Banankoro
Guinea (GIN) = ± s min = City population, log s C i t y G D P , l o g y Conakry
Kankan
Nzérékoré
Kindia
Siguiri
Labé
Kamsar
Kissidougou
Faranah
Mamou
Sangarédi
Sinko
Macenta
Guéckédou
Boké
Banankoro
Guinea (GIN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Greece (GRC) = ± s min = City population, log s C i t y r an k , l o g r Athens
Thessaloniki
Patras
Heraklion
Larissa
Volos
Ioannina
Chania
Chalkida
Greece (GRC) = ± s min = City population, log s C i t y G D P , l o g y Athens
Thessaloniki
Patras
Heraklion
Larissa
Volos
Ioannina
Chania
Chalkida
Greece (GRC) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Guatemala (GTM) = ± s min = City population, log s C i t y r an k , l o g r Guatemala City
Cobán
Quetzaltenango
Chimaltenango
San Pedro Sacatepéquez [San Marcos]
Escuintla
Totonicapán
Huehuetenango
Jalapa
Mazatenango
Santa Cruz Barillas
Flores
Santa Cruz del Quiché
Coatepeque
Jutiapa
Santa Lucía Cotzumalguapa
Malacatán
Retalhuleu
Ciudad Vieja [Antigua Guatemala]
Panajachel [Sololá]
Chichicastenango
Chiquimula
Puerto Barrios
Playa Grande Ixcán
Morales
Santa María Nebaj
Aguacatán
Joyabaj
Cubulco
Poptún
San Cristobal Verapaz
Fray Bartolomé de las Casas
El Estor
Guatemala (GTM) = ± s min = City population, log s C i t y G D P , l o g y Guatemala City
Cobán
Quetzaltenango
Chimaltenango
San Pedro Sacatepéquez [San Marcos]
Escuintla
Totonicapán
Huehuetenango
Jalapa
Mazatenango
Santa Cruz Barillas
Flores
Santa Cruz del Quiché
Coatepeque
Jutiapa
Santa Lucía Cotzumalguapa
Malacatán
Retalhuleu
Ciudad Vieja [Antigua Guatemala]
Panajachel [Sololá]
Chichicastenango
Chiquimula
Puerto Barrios
Playa Grande Ixcán
Morales
Santa María Nebaj
Aguacatán
Joyabaj
Cubulco
Poptún
San Cristobal Verapaz
Fray Bartolomé de las Casas
El Estor
Guatemala (GTM) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Honduras (HND) = ± s min = City population, log s C i t y r an k , l o g r Tegucigalpa
San Pedro Sula
La Ceiba
Choluteca
Villanueva
El Progreso
Comayagua
Puerto Cortés
Barrio El Centro
Siguatepeque
Danli
Santa Rosa
Honduras (HND) = ± s min = City population, log s C i t y G D P , l o g y Tegucigalpa
San Pedro Sula
La Ceiba
Choluteca
Villanueva
El Progreso
Comayagua
Puerto Cortés
Barrio El Centro
Siguatepeque
Danli
Santa Rosa
Honduras (HND) = ± .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Haiti (HTI) = ± s min = City population, log s C i t y r an k , l o g r Port-au-Prince
Gonaïves
Cap-Haitien
Saint-Marc
Petit-Goâve
Léogâne
Port-de-Paix
Jacmel
Saint-Louis-du-Nord
Anse-à-Galets
Les Cayes
Ouanaminthe
Hinche
Gros Morne
Saint Michel de lAttalaye
Dessalines
La Croix
Jérémie
Mirebalais
Petite-Rivière-de-l'Artibonite
Haiti (HTI) = ± s min = City population, log s C i t y G D P , l o g y Port-au-Prince
Gonaïves
Cap-Haitien
Saint-Marc
Petit-Goâve
Léogâne
Port-de-Paix
Jacmel
Saint-Louis-du-Nord
Anse-à-Galets
Les Cayes
Ouanaminthe
Hinche
Gros Morne
Saint Michel de lAttalaye
Dessalines
La Croix
Jérémie
Mirebalais
Petite-Rivière-de-l'Artibonite
Haiti (HTI) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Hungary (HUN) = ± s min = City population, log s C i t y r an k , l o g r Budapest
Debrecen
Miskolc
Szeged
Pécs
Gy r
Nyíregyháza
Hungary (HUN) = ± s min = City population, log s C i t y G D P , l o g y Budapest
Debrecen
Miskolc
Szeged
Pécs
Gy r
Nyíregyháza
Hungary (HUN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Indonesia (IDN) = ± s min = City population, log s C i t y r an k , l o g r Jakarta
Surabaya
Bandung
Yogyakarta
Medan
Jombang
Semarang
Jakarta
Tegal
Purwokerto
Jakarta
Cirebon
Makassar
Denpasar
Tasikmalaya
Pati
Garut
Jember
Palembang
Jakarta
Madiun
Jakarta
Pekalongan
Bandar Lampung
Banjarmasin
Mataram
Samarinda
Pekanbaru
Mojokerto
Magelang
Padang
Batam City
Temanggung
Jambi
Pontianak
Selong
Tulungagung
Kuningan
Cilegon
Probolinggo
Cilacap
Lumajang
Balikpapan
Pamekasan
Kebumen
Sumenep
Gorontalo
Indramayu
Metro
Subang
Manado
Trenggalek
Singaraja
Kendari
Kupang
Banda Aceh
Bangkalan
Rangkasbitung
Pematang Siantar
Purwodadi
Bojonegoro
Purworejo
Bukittinggi
Kel Rijali
Bengkulu
Sampang
Pandeglang
Palu
Pangkalpinang
Bondowoso
Ketapang
Sampit
Timika
Padang Sidempuan
Sragen
Pacitan
Ruteng
Palabuhanratu
Gunung Sugih
Tanjung Balai
Dumai
Sintang
Tebing Tinggi
Sangatta
Banyuwangi
Tuban
Genteng
Muncar
Sorong
Mamuju
Tarakan
Duri
Pringsewu
Muara Bungo
Waingapu
Tambolaka
Bitung
Singkawang
Blora
Situbondo
Rantau Prapat
Kisaran
Pemangkat
Sumbawa Besar
Pandan
Takatidung
Bulukumba
Merauke
Luwuk
Watampone
Ternate
Mekarjaya
Wonosari
Jayapura
Kuala Kapuas
Lubuklinggau
Rantepao
Sumuradem
Wates
Curup
Ende
Raha
Maumere
Banjar
Babat
Pangkajene
Langsa
Kogimage
Kotabumi
Pare-Pare
Kotamobagu
Labuan Bajo
Amuntai
Purworejo
Tembilahan
Manokwari
Lahat
Bireuen
Kolaka
Panyabungan
Sengkang
Baubau
Negara
Prabumulih
Nabire
Palopo
Bima
Payakumbuh
Kotabaru
Balangnipa
Ciherang
Lamongan
Biak Kota
Poso
Dompu
Sigli
Asembagus
Gunungsitoli
Tanjung Enim
Mekarjaya
Nanga Pinoh
Semurup
Toboali
Bagan Siapi-api
Kalianda
Tanjung Redeb
Kalabahi
Tanjung Balai Karimun
Atambua
Sentani
Bangko
Ngawi
Kandangan
Ngabang
Rembang
Tolitoli
Palangka Raya
Pinrang
Masohi
Ampana
Lhokseumawe
Lepar Samura
Tarutung
Bantaeng
Tanjung Pandan
Solok
Pagojengan
Batu Licin
Tobelo
Perawang
Sidogede
Sidikalang
Selatpanjang
Tebing Suluh
Barabai
Muara Enim
Ujung Batu
Marabahan
Besuki
Uteun Geulinggang
Muaratewe
Bontang
Serui Kota
Pagar Alam
Unit 1
Sidorejo
Kuala Tungkal
Pangkalan Kerinci
Kotaraja
Parigi
Majene
Gunung Tua
Pangkajene
Baturaja
Buol
Meulaboh
Pangkalan Brandan
Teluk Dalam
Tomohon
Nunukan
Tondano
Manna
Pasangkayu
Arga Makmur
Bajawa
Sarolangun
Indonesia (IDN) = ± s min = City population, log s C i t y G D P , l o g y Jakarta
Surabaya
Bandung
Yogyakarta
Medan
Jombang
Semarang
Jakarta
Tegal
Purwokerto
Jakarta
Cirebon
Makassar
Denpasar
Tasikmalaya
Pati
Garut
Jember
Palembang
Jakarta
Madiun
Jakarta
Pekalongan
Bandar Lampung
Banjarmasin
Mataram
Samarinda
Pekanbaru
Mojokerto
Magelang
Padang
Batam City
Temanggung
Jambi
Pontianak
Selong
Tulungagung
Kuningan
Cilegon
Probolinggo
Cilacap
Lumajang
Balikpapan
Pamekasan
Kebumen
Sumenep
Gorontalo
Indramayu
Metro
Subang
Manado
Trenggalek
Singaraja
Kendari
Kupang
Banda Aceh
Bangkalan
Rangkasbitung
Pematang Siantar
Purwodadi
Bojonegoro
Purworejo
Bukittinggi
Kel Rijali
Bengkulu
Sampang
Pandeglang
Palu
Pangkalpinang
Bondowoso
Ketapang
Sampit
Timika
Padang Sidempuan
Sragen
Pacitan
Ruteng
Palabuhanratu
Gunung Sugih
Tanjung Balai
Dumai
Sintang
Tebing Tinggi
Sangatta
Banyuwangi
Tuban
Genteng
Muncar
Sorong
Mamuju
Tarakan
Duri
Pringsewu
Muara Bungo
Waingapu
Tambolaka
Bitung
Singkawang
Blora
Situbondo
Rantau Prapat
Kisaran
Pemangkat
Sumbawa Besar
Pandan
Takatidung
Bulukumba
Merauke
Luwuk
Watampone
Ternate
Mekarjaya
Wonosari
Jayapura
Kuala Kapuas
Lubuklinggau
Rantepao
Sumuradem
Wates
Curup
Ende
Raha
Maumere
Banjar
Babat
Pangkajene
Langsa
Kogimage
Kotabumi
Pare-Pare
Kotamobagu
Labuan Bajo
Amuntai
Purworejo
Tembilahan
Manokwari
Lahat
Bireuen
Kolaka
Panyabungan
Sengkang
Baubau
Negara
Prabumulih
Nabire
Palopo
Bima
Payakumbuh
Kotabaru
Balangnipa
Ciherang
Lamongan
Biak Kota
Poso
Dompu
Sigli
Asembagus
Gunungsitoli
Tanjung Enim
Mekarjaya
Nanga Pinoh
Semurup
Toboali
Bagan Siapi-api
Kalianda
Tanjung Redeb
Kalabahi
Tanjung Balai Karimun
Atambua
Sentani
Bangko
Ngawi
Kandangan
Ngabang
Rembang
Tolitoli
Palangka Raya
Pinrang
Masohi
Ampana
Lhokseumawe
Lepar Samura
Tarutung
Bantaeng
Tanjung Pandan
Solok
Pagojengan
Batu Licin
Tobelo
Perawang
Sidogede
Sidikalang
Selatpanjang
Tebing Suluh
Barabai
Muara Enim
Ujung Batu
Marabahan
Besuki
Uteun Geulinggang
Muaratewe
Bontang
Serui Kota
Pagar Alam
Unit 1
Sidorejo
Kuala Tungkal
Pangkalan Kerinci
Kotaraja
Parigi
Majene
Gunung Tua
Pangkajene
Baturaja
Buol
Meulaboh
Pangkalan Brandan
Teluk Dalam
Tomohon
Nunukan
Tondano
Manna
Pasangkayu
Arga Makmur
Bajawa
Sarolangun
Indonesia (IDN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) India (IND) = ± s min = City population, log s C i t y r an k , l o g r Delhi [New Delhi]
Kolkata
Mumbai
Bengaluru
Chennai
Hyderabad
Ahmedabad
Pune
Surat
Lucknow
Varanasi
Kanpur
Kochi
Jaipur
Asansol
Indore
Prayagraj
Nagpur
Patna
Guruvayur
Thiruvananthapuram
Kollam
Agra
Coimbatore
Kozhikode
Chandigarh
Meerut
Vadodara
Bhopal
Dhanbad
Gorakhpur
Tamluk
Ludhiana
Madurai
Faizabad
Muzaffarpur
Nashik
Visakhapatnam
Aurangabad
Moradabad
Salem
Jamshedpur
Ranchi
Bareilly
Aligarh
Jabalpur
Kuchai Kot
Kannur
Gwalior
Raipur
Berhampore
Erode
Mangaluru
Jodhpur
Vijayawada
Tiruppur
Kolkata
Vasai-Virar
Thalassery
Mysuru
Rajkot
Tiruchirappalli
Guwahati
Amritsar
Vellore
Ettumanoor
Srinagar
Saharanpur
Sultanpur
Durg
Hardoi
Jalandhar
Malappuram
Dehradun
Bhubaneshwar
Jammu
Begusarai
Kota
Solapur
Silvassa
Imphal
Gonda
Haridwar
Kolhapur
Shahjahanpur
Gaya
Farrukhabad
Sangli
Bilaspur
Puducherry
Lakhimpur
Fatehpur
Muzaffarnagar
Mirzapur
Dhing
Krishnanagar
Nibua Raiganj
Bahraich
Guntur
Cuttack
Mathura
Bokaro
Alappuzha
Jaunpur
Belagavi
Firozabad
Thrissur
Kushinagar
Pratapgarh
Udaipur
Dharwad
Warangal
Sitapur
Malegaon
Bikaner
Agartala
Anantnag
Darbhanga
Rae Bareli
Nagercoil
Alwar
Nellore
Jalpaiguri
Kalaburagi
Basti
Anand
Sambhal
Ambala
Sagar
Amravati
Kharagpur
Nanded-Waghala
Budaun
Rourkela
Jamnagar
Siliguri
Deoria
Mau
Yamunanagar
Jalgaon
Neeleshwaram
Raiganj
Patiala
Canning
Jhansi
Ballia
Bhavnagar
Akola
Etawah
Panipat
Bhadohi
Piprakothi
Dhule
Balrampur
Azamgarh
Jaynagar Majilpur
Pilibhit
Bihar Sharif
Sitamarhi
Nanpara
Banda
Silchar
Kharupetia
Rampur
Mainpuri
Dhulian
Ballari
Bhiwadi
Ahmadnagar
Davanagere
Tirupati
Lauiyah Nandangarh
Unnao
Bulandshahr
Ajmer
Ghazipur
Giridih
Sandila
Tulsipur
Dindigul
Etah
Jangipur
Chhapra
Vijayapura
Darjeeling
Brahmapur
Rohtak
Amroha
Katihar
Ujjain
Munger
Rajamahendravaram
Waidhan
Bettiah
Sansarpur
Samastipur
Dimapur
Gandhidham
Deesa
Tumakuru
Hisar
Sikar
Latur
Bhinga
Satna
Khalilabad
Mansa Nagar
Kakinada
Palakkad
Bhind
Dhupguri
Kurnool
Purnia
Thakurdwara
Saharsa
Shahabad
Shillong
Hathras
Haldwani
UNNAMED
Deoghar
Obra
Cooch Behar
Dahod
Arrah
Khaga
Chitrakoot Dham
Shivamogga
Naugarh
Akbarpur
Nadiad
Hajipur
Morena
Thoothukudi
Dharmapuri
Banswara
Lalitpur
Anantapur
Shikohabad
Siuri
Chandausi
Colonelganj
Mahesana
Nagapattinam
Kumbakonam
Rewa, Madhya Pradesh
Roorkee
Khurja
Puruliya
Korba
Jalna
Bhilwara
NizamabadThanjavur
UNNAMED
Sidhauli
Bhiwani
Utraula
Parbhani
Tiruvannamalai
Rajapalaiyam
Chandrapur
Bharatpur
Hindaun
Beed
Maharajganj
Godhra
KhandwaIchalkaranji
Phalodi
Karnal
Bathinda
Nawab Ganj
Tanda
Kanchipuram
EluruBharuch
Dhubri
Gopiganj
Kolar Gold Fields
Jalalpur
Barmer
BidarDobhi
Baheri
Navsari
Rudrapur
Tirunelveli
KaimganjMuhammadabad
Damoh
Maholi
Ratlam
KhammamBalotra
Dausa
Mohmadi
Tezpur
KatniTinsukia
Chhibramau
Lalganj
SidhiDewas
Palanpur
Shahganj
BaberuMandya
Cuddalore
Sasaram
JolarpetBhagalpur
Sirsa
Bankura
TilharKadapa
Medininagar
Chitradurga
BisalpurKarimnagar
Karur
BansiMirganj
Orai
Chhatarpur
DurgapurKurukshetra
Dhaulpur
DatiaPanaji
Nautanwa
ViluppuramSurendranagar
Vizianagaram
PatanValsad
Yavatmal
HassanJunagadh
Burhanpur
BeawarKishangarh
Gangapur
BuxarGuna
Rafiganj
BatalaBasirhat
Narkatiaganj
MusiriKunda
SiwanShivpuri
Chhindwara
Anand NagarMasaurhi
Sangamner
JouraMorbi
RajsamandMandi Gobindgarh
Satara
MuhammadabadRudauli
AmethiAliganj
Kannauj
AizawlNotun Digha
ContaiPali
Bilari
SivaniLaharpur
BoisarKasganj
ChittorgarhNeyveli
Alirajpur
KarauliEtmadpur
NawadaBhadravathi
DehriManjha
Jhumri Tilaiya
SingrauliNawabganj
RaichurBandikui
PorbandarKalpi
MotihariMahuva
Gauriganj
PollachiBhongaon
BhusawalDoddaballapura
PuriKrishnagiri
MadhubaniAuraiya
BijnorAmbikapur
UdupiWardha
VidishaHazaribagh
Habra
FaridpurSawai Madhopur
NanjanaguduNajibabad
DungarpurSujangarh
KishanganjGudiyatham
SalonRanaghat
BhadrakRasra
India (IND) = ± s min = City population, log s C i t y G D P , l o g y Delhi [New Delhi]
Kolkata
Mumbai
Bengaluru
Chennai
Hyderabad
Ahmedabad
Pune
Surat
Lucknow
Varanasi
Kanpur
Kochi
Jaipur
Asansol
Indore
Prayagraj
Nagpur
Patna
Guruvayur
Thiruvananthapuram
Kollam
Agra
Coimbatore
Kozhikode
Chandigarh
Meerut
Vadodara
Bhopal
Dhanbad
Gorakhpur
Tamluk
Ludhiana
Madurai
Faizabad
Muzaffarpur
Nashik
Visakhapatnam
Aurangabad
Moradabad
Salem
Jamshedpur
Ranchi
Bareilly
Aligarh
Jabalpur
Kuchai Kot
Kannur
Gwalior
Raipur
Berhampore
Erode
Mangaluru
Jodhpur
Vijayawada
Tiruppur
Kolkata
Vasai-Virar
Thalassery
Mysuru
Rajkot
Tiruchirappalli
Guwahati
Amritsar
Vellore
Ettumanoor
Srinagar
Saharanpur
Sultanpur
Durg
Hardoi
Jalandhar
Malappuram
Dehradun
Bhubaneshwar
Jammu
Begusarai
Kota
Solapur
Silvassa
Imphal
Gonda
Haridwar
Kolhapur
Shahjahanpur
Gaya
Farrukhabad
Sangli
Bilaspur
Puducherry
Lakhimpur
Fatehpur
Muzaffarnagar
Mirzapur
Dhing
Krishnanagar
Nibua Raiganj
Bahraich
Guntur
Cuttack
Mathura
Bokaro
Alappuzha
Jaunpur
Belagavi
Firozabad
Thrissur
Kushinagar
Pratapgarh
Udaipur
Dharwad
Warangal
Sitapur
Malegaon
Bikaner
Agartala
Anantnag
Darbhanga
Rae Bareli
Nagercoil
Alwar
Nellore
Jalpaiguri
Kalaburagi
Basti
Anand
Sambhal
Ambala
Sagar
Amravati
Kharagpur
Nanded-Waghala
Budaun
Rourkela
Jamnagar
Siliguri
Deoria
Mau
Yamunanagar
Jalgaon
Neeleshwaram
Raiganj
Patiala
Canning
Jhansi
Ballia
Bhavnagar
Akola
Etawah
Panipat
Bhadohi
Piprakothi
Dhule
Balrampur
Azamgarh
Jaynagar Majilpur
Pilibhit
Bihar Sharif
Sitamarhi
Nanpara
Banda
Silchar
Kharupetia
Rampur
Mainpuri
Dhulian
Ballari
Bhiwadi
Ahmadnagar
Davanagere
Tirupati
Lauiyah Nandangarh
Unnao
Bulandshahr
Ajmer
Ghazipur
Giridih
Sandila
Tulsipur
Dindigul
Etah
Jangipur
Chhapra
Vijayapura
Darjeeling
Brahmapur
Rohtak
Amroha
Katihar
Ujjain
Munger
Rajamahendravaram
Waidhan
Bettiah
Sansarpur
Samastipur
Dimapur
Gandhidham
Deesa
Tumakuru
Hisar
Sikar
Latur
Bhinga
Satna
Khalilabad
Mansa Nagar
Kakinada
Palakkad
Bhind
Dhupguri
Kurnool
Purnia
Thakurdwara
Saharsa
Shahabad
Shillong
Hathras
Haldwani
UNNAMED
Deoghar
Obra
Cooch Behar
Dahod
Arrah
Khaga
Chitrakoot Dham
Shivamogga
Naugarh
Akbarpur
Nadiad
Hajipur
Morena
Thoothukudi
Dharmapuri
Banswara
Lalitpur
Anantapur
Shikohabad
Siuri
Chandausi
Colonelganj
Mahesana
Nagapattinam
Kumbakonam
Rewa, Madhya Pradesh
Roorkee
Khurja
Puruliya
Korba
Jalna
Bhilwara
NizamabadThanjavur
UNNAMED
Sidhauli
Bhiwani
Utraula
Parbhani
Tiruvannamalai
Rajapalaiyam
Chandrapur
Bharatpur
Hindaun
Beed
Maharajganj
Godhra
KhandwaIchalkaranji
Phalodi
Karnal
Bathinda
Nawab Ganj
Tanda
Kanchipuram
EluruBharuch
Dhubri
Gopiganj
Kolar Gold Fields
Jalalpur
Barmer
BidarDobhi
Baheri
Navsari
Rudrapur
Tirunelveli
KaimganjMuhammadabad
Damoh
Maholi
Ratlam
KhammamBalotra
Dausa
Mohmadi
Tezpur
KatniTinsukia
Chhibramau
Lalganj
SidhiDewas
Palanpur
Shahganj
BaberuMandya
Cuddalore
Sasaram
JolarpetBhagalpur
Sirsa
Bankura
TilharKadapa
Medininagar
Chitradurga
BisalpurKarimnagar
Karur
BansiMirganj
Orai
Chhatarpur
DurgapurKurukshetra
Dhaulpur
DatiaPanaji
Nautanwa
ViluppuramSurendranagar
Vizianagaram
PatanValsad
Yavatmal
HassanJunagadh
Burhanpur
BeawarKishangarh
Gangapur
BuxarGuna
Rafiganj
BatalaBasirhat
Narkatiaganj
MusiriKunda
SiwanShivpuri
Chhindwara
Anand NagarMasaurhi
Sangamner
JouraMorbi
RajsamandMandi Gobindgarh
Satara
MuhammadabadRudauli
AmethiAliganj
Kannauj
AizawlNotun Digha
ContaiPali
Bilari
SivaniLaharpur
BoisarKasganj
ChittorgarhNeyveli
Alirajpur
KarauliEtmadpur
NawadaBhadravathi
DehriManjha
Jhumri Tilaiya
SingrauliNawabganj
RaichurBandikui
PorbandarKalpi
MotihariMahuva
Gauriganj
PollachiBhongaon
BhusawalDoddaballapura
PuriKrishnagiri
MadhubaniAuraiya
BijnorAmbikapur
UdupiWardha
VidishaHazaribagh
Habra
FaridpurSawai Madhopur
NanjanaguduNajibabad
DungarpurSujangarh
KishanganjGudiyatham
SalonRanaghat
BhadrakRasra
India (IND) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Iran (IRN) = ± s min = City population, log s C i t y r an k , l o g r Tehran
Mashhad
Isfahan
Tabriz
Shiraz
Ahwaz
Qom
Kermanshah
Urmia
Rasht
Hamedan
Zahedan
Kerman
Yazd
Ardabil
Arak
Bandar Abbas
Dezful
Qarchak
Zanjan
Sanandaj
Qazvin
Khorramabad
Gorgan
Abadan
Sari
Jiroft
Bojnurd
Babol
Kashan
Neyshabur
Gonbad-e Qabus
Pardis
Amol
Chabahar
Qaem Shahr
Borujerd
Birjand
Sirjan
Yasuj
Najafabad
Khoy
Chalus
Bagh-e Zahra
Pakdasht
Miandoab
Maragheh
Malayer
Shoushtar
Sabzevar
Rafsanjan
Saqqez
Zabol
Izeh
Ilam
Saveh
Mahabad
Kazerun
Jahrom
Shahrud
Ardakan
Marvdasht
Kuhdasht
Quchan
Marivan
Iranshahr
Lahijan
Shahr-e Kord
Shirvan
Bam
Kashmar
Baneh
Semnan
Salmas
Shahreza
Eslamabad-e Gharb
Aligudarz
Darab
Shahin Shahr
Torbat-e Jam
Fasa
Bandar-e Anzali
Behbahan
Ahar
Khash
Dorud
Bandar-e Mahshahr
Marand
Shadegan
Alvand
Nurabad
Zarrinshahr
Esfarayen
Mianeh
Talesh
Bonab
Dogonbadan
Nahavand
Nazarabad
Iran (IRN) = ± s min = City population, log s C i t y G D P , l o g y Tehran
Mashhad
Isfahan
Tabriz
Shiraz
Ahwaz
Qom
Kermanshah
Urmia
Rasht
Hamedan
Zahedan
Kerman
Yazd
Ardabil
Arak
Bandar Abbas
Dezful
Qarchak
Zanjan
Sanandaj
Qazvin
Khorramabad
Gorgan
Abadan
Sari
Jiroft
Bojnurd
Babol
Kashan
Neyshabur
Gonbad-e Qabus
Pardis
Amol
Chabahar
Qaem Shahr
Borujerd
Birjand
Sirjan
Yasuj
Najafabad
Khoy
Chalus
Bagh-e Zahra
Pakdasht
Miandoab
Maragheh
Malayer
Shoushtar
Sabzevar
Rafsanjan
Saqqez
Zabol
Izeh
Ilam
Saveh
Mahabad
Kazerun
Jahrom
Shahrud
Ardakan
Marvdasht
Kuhdasht
Quchan
Marivan
Iranshahr
Lahijan
Shahr-e Kord
Shirvan
Bam
Kashmar
Baneh
Semnan
Salmas
Shahreza
Eslamabad-e Gharb
Aligudarz
Darab
Shahin Shahr
Torbat-e Jam
Fasa
Bandar-e Anzali
Behbahan
Ahar
Khash
Dorud
Bandar-e Mahshahr
Marand
Shadegan
Alvand
Nurabad
Zarrinshahr
Esfarayen
Mianeh
Talesh
Bonab
Dogonbadan
Nahavand
Nazarabad
Iran (IRN) = ± .0 6.2 6.4 6.6 6.8 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Iraq (IRQ) = ± s min = City population, log s C i t y r an k , l o g r Baghdad
Basra
Erbil
Mosul
Najaf
Ad Diwaniyah
Hindiya
Kirkuk
Karbala
Iraq (IRQ) = ± s min = City population, log s C i t y G D P , l o g y Baghdad
Basra
Erbil
Mosul
Najaf
Ad Diwaniyah
Hindiya
Kirkuk
Karbala
Iraq (IRQ) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Italy (ITA) = ± s min = City population, log s C i t y r an k , l o g r Milan
Naples
Rome
Turin
Florence
Bergamo
Palermo
Catania
Genoa
Padua
Bologna
Bari
Brescia
Verona
Pescara
Mestre
Salerno
Cagliari
Vicenza
Modena
Como
Rimini
Treviso
Taranto
Messina
Udine
Parma
Triest
Reggio nell'Emilia
Reggio Calabria
Massa
Pordenone
Trento
Cosenza
Lecco
Anzio
Italy (ITA) = ± s min = City population, log s C i t y G D P , l o g y Milan
Naples
Rome
Turin
Florence
Bergamo
Palermo
Catania
Genoa
Padua
Bologna
Bari
Brescia
Verona
Pescara
Mestre
Salerno
Cagliari
Vicenza
Modena
Como
Rimini
Treviso
Taranto
Messina
Udine
Parma
Triest
Reggio nell'Emilia
Reggio Calabria
Massa
Pordenone
Trento
Cosenza
Lecco
Anzio
Italy (ITA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Japan (JPN) = ± s min = City population, log s C i t y r an k , l o g r Tokyo
Osaka [Kyoto]
Nagoya
Fukuoka
Takasaki [Maebashi]
Sapporo
Hiroshima
Kitakyushu
Sendai
Okayama
Naha
Shizuoka
Hamamatsu
Kumamoto
Mishima
Mito
Niigata
Toyama
Utsunomiya
Moriyama [Otsu]
Toyohashi
Takamatsu
Kanazawa
Tokushima
Fukuyama
Kagoshima
Kinokawa [Wakayama]
Matsuyama
Japan (JPN) = ± s min = City population, log s C i t y G D P , l o g y Tokyo
Osaka [Kyoto]
Nagoya
Fukuoka
Takasaki [Maebashi]
Sapporo
Hiroshima
Kitakyushu
Sendai
Okayama
Naha
Shizuoka
Hamamatsu
Kumamoto
Mishima
Mito
Niigata
Toyama
Utsunomiya
Moriyama [Otsu]
Toyohashi
Takamatsu
Kanazawa
Tokushima
Fukuyama
Kagoshima
Kinokawa [Wakayama]
Matsuyama
Japan (JPN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Kazakhstan (KAZ) = ± s min = City population, log s C i t y r an k , l o g r Almaty
Shymkent
Nur-Sultan
Aktobe
Karaganda
Semey
Pavlodar
Oskemen
Taraz
Aktau
Oral
Kyzylorda
Atyrau
Turkestan
Kazakhstan (KAZ) = ± s min = City population, log s C i t y G D P , l o g y Almaty
Shymkent
Nur-Sultan
Aktobe
Karaganda
Semey
Pavlodar
Oskemen
Taraz
Aktau
Oral
Kyzylorda
Atyrau
Turkestan
Kazakhstan (KAZ) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Kenya (KEN) = ± s min = City population, log s C i t y r an k , l o g r Nairobi
Mombasa
Nakuru
Eldoret
Kisumu
Kisii
Garissa
Kitale
Thika
Ongata Rongai
Malindi
Mandera
Kakamega
El Wak
Kitengela
Wajir
Hagadera Refugee Camp
Nyeri
Bungoma
Meru
Dadaab
Machakos
Embu
Busia
Naivasha
Mtwapa
Nyahururu
Kakuma
Ukunda
Kimilili
Kilifi
Kenya (KEN) = ± s min = City population, log s C i t y G D P , l o g y Nairobi
Mombasa
Nakuru
Eldoret
Kisumu
Kisii
Garissa
Kitale
Thika
Ongata Rongai
Malindi
Mandera
Kakamega
El Wak
Kitengela
Wajir
Hagadera Refugee Camp
Nyeri
Bungoma
Meru
Dadaab
Machakos
Embu
Busia
Naivasha
Mtwapa
Nyahururu
Kakuma
Ukunda
Kimilili
Kilifi
Kenya (KEN) = ± .5 6.0 6.5 7.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) South Korea (KOR) = ± s min = City population, log s C i t y r an k , l o g r Seoul
Busan
Daegu
Daejeon
Gwangju
Ulsan
Cheongju-si
Cheonan-si
Changwon
Jeonju
Pohang-si
Gumi-si
Jinju-si
Mokpo-si
Dongducheon-si
Wonju-si
Suncheon-si
Chuncheon-si
Gunsan-si
Iksan-si
Geoje-si
Jeju-si
South Korea (KOR) = ± s min = City population, log s C i t y G D P , l o g y Seoul
Busan
Daegu
Daejeon
Gwangju
Ulsan
Cheongju-si
Cheonan-si
Changwon
Jeonju
Pohang-si
Gumi-si
Jinju-si
Mokpo-si
Dongducheon-si
Wonju-si
Suncheon-si
Chuncheon-si
Gunsan-si
Iksan-si
Geoje-si
Jeju-si
South Korea (KOR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Libya (LBY) = ± s min = City population, log s C i t y r an k , l o g r Tripoli
Benghazi
Misrata
Al Zawiyah
Qabilat alturki
Zliten
Tobruk
Sabha
Bayda
Marj
Sirte
Derna
Libya (LBY) = ± s min = City population, log s C i t y G D P , l o g y Tripoli
Benghazi
Misrata
Al Zawiyah
Qabilat alturki
Zliten
Tobruk
Sabha
Bayda
Marj
Sirte
Derna
Libya (LBY) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Sri Lanka (LKA) = ± s min = City population, log s C i t y r an k , l o g r Colombo
Kandy
Matara
Galle
Jaffna
Kalmunai
Batticaloa
Trincomalee
Ambalangoda
Badulla
Sri Lanka (LKA) = ± s min = City population, log s C i t y G D P , l o g y Colombo
Kandy
Matara
Galle
Jaffna
Kalmunai
Batticaloa
Trincomalee
Ambalangoda
Badulla
Sri Lanka (LKA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Morocco (MAR) = ± s min = City population, log s C i t y r an k , l o g r Casablanca
Rabat
Fez
Marrakesh
Agadir
Tangier
Meknes
Oujda
Kenitra
Tétouan
Safi
Nador
El Jadida
Beni Mellal
Khouribga
Taza
Ksar el-Kebir
Khemisset
Settat
Berkane
Berrechid
Khenifra
Sidi Slimane
Larache
Guelmim
Guercif
El Kelaa des Sraghna
Fkih Ben Salah
Taourirt
Oued Zem
Errachidia
Ouarzazate
Sefrou
Sidi Bennour
Souk El Arba Du Gharb
Sidi Kacem
Tiflet
Ben Guerir
Youssoufia
Azemmour
Tiznit
Deroua
Ouazzane
Melilla
Ceuta
Souk Sebt Oulad Nemma
Essaouira
Kasba Tadla
Taroudant
Zagora
Chefchaouen
Azrou
Midelt
Sidi Yahya du Gharb
Ouled-Teima
Al Hoceima
Ain Taoujdate
Ain El Aouda
Bejaad
Morocco (MAR) = ± s min = City population, log s C i t y G D P , l o g y Casablanca
Rabat
Fez
Marrakesh
Agadir
Tangier
Meknes
Oujda
Kenitra
Tétouan
Safi
Nador
El Jadida
Beni Mellal
Khouribga
Taza
Ksar el-Kebir
Khemisset
Settat
Berkane
Berrechid
Khenifra
Sidi Slimane
Larache
Guelmim
Guercif
El Kelaa des Sraghna
Fkih Ben Salah
Taourirt
Oued Zem
Errachidia
Ouarzazate
Sefrou
Sidi Bennour
Souk El Arba Du Gharb
Sidi Kacem
Tiflet
Ben Guerir
Youssoufia
Azemmour
Tiznit
Deroua
Ouazzane
Melilla
Ceuta
Souk Sebt Oulad Nemma
Essaouira
Kasba Tadla
Taroudant
Zagora
Chefchaouen
Azrou
Midelt
Sidi Yahya du Gharb
Ouled-Teima
Al Hoceima
Ain Taoujdate
Ain El Aouda
Bejaad
Morocco (MAR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Mexico (MEX) = ± s min = City population, log s C i t y r an k , l o g r Mexico City
Guadalajara
Monterrey
Puebla
Toluca
Tijuana
León
Ciudad Juárez
Torreon
Querétaro
San Luis Potosí
Cuernavaca
Mérida
Aguascalientes
Mexico (MEX) = ± s min = City population, log s C i t y G D P , l o g y Mexico City
Guadalajara
Monterrey
Puebla
Toluca
Tijuana
León
Ciudad Juárez
Torreon
Querétaro
San Luis Potosí
Cuernavaca
Mérida
Aguascalientes
Mexico (MEX) = ± .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Mali (MLI) = ± s min = City population, log s C i t y r an k , l o g r Bamako
Sikasso
Ségou
Koutiala
Kayes
Socoura
Gao
Niono
San
Timbuktu
Kita
Bougouni
Mopti
Mali (MLI) = ± s min = City population, log s C i t y G D P , l o g y Bamako
Sikasso
Ségou
Koutiala
Kayes
Socoura
Gao
Niono
San
Timbuktu
Kita
Bougouni
Mopti
Mali (MLI) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Myanmar (MMR) = ± s min = City population, log s C i t y r an k , l o g r Yangon
Mandalay
Myitkyina
Bago
Myeik
Taunggyi
Naypyidaw
Pathein
Lashio
Mawlamyine
Hinthada
Myaungmya
Monywa
Meiktila
Hpa-An
Mawlamyinegyunn
Pyin Oo Lwin
Pyay
Taungoo
Labutta
Kyaiklat
Magway
Wakema
Myingyan
Thaton
Pantanaw
Kengtung
Sittwe
UNNAMED
Pakokku
Danu Phyu
Pyapon
Za Lun
Dawei
Aunglan
Maubin
Tangyan
Tan Soe
Tachileik
Minbya
Myawaddy
Loikaw
Wundwin
Taungup
Pyawbwe
Pyu
Shwebo
Kayan
Daik-U
Mogok
Aungpan
Nyaunglebin
Hsipaw
Thongwa
Mudon
Kyaikto
Twante
Kyaukme
Kawthaung
Myan Aung
Muse
Yamethin
Kyaukpadaung
Nattalin
Hlegu
Nyaung Shwe
Payathonzu
Shwegyin
Bhamo
Hopong
UNNAMED
Dedaye
Madaya
Taungdwingyi
Tatkon
Ngathaingchaung
Myanmar (MMR) = ± s min = City population, log s C i t y G D P , l o g y Yangon
Mandalay
Myitkyina
Bago
Myeik
Taunggyi
Naypyidaw
Pathein
Lashio
Mawlamyine
Hinthada
Myaungmya
Monywa
Meiktila
Hpa-An
Mawlamyinegyunn
Pyin Oo Lwin
Pyay
Taungoo
Labutta
Kyaiklat
Magway
Wakema
Myingyan
Thaton
Pantanaw
Kengtung
Sittwe
UNNAMED
Pakokku
Danu Phyu
Pyapon
Za Lun
Dawei
Aunglan
Maubin
Tangyan
Tan Soe
Tachileik
Minbya
Myawaddy
Loikaw
Wundwin
Taungup
Pyawbwe
Pyu
Shwebo
Kayan
Daik-U
Mogok
Aungpan
Nyaunglebin
Hsipaw
Thongwa
Mudon
Kyaikto
Twante
Kyaukme
Kawthaung
Myan Aung
Muse
Yamethin
Kyaukpadaung
Nattalin
Hlegu
Nyaung Shwe
Payathonzu
Shwegyin
Bhamo
Hopong
UNNAMED
Dedaye
Madaya
Taungdwingyi
Tatkon
Ngathaingchaung
Myanmar (MMR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Mozambique (MOZ) = ± s min = City population, log s C i t y r an k , l o g r Maputo
Nampula
Milange
Beira
Chimoio
Nacala
Quelimane
Tete
Mozambique (MOZ) = ± s min = City population, log s C i t y G D P , l o g y Maputo
Nampula
Milange
Beira
Chimoio
Nacala
Quelimane
Tete
Mozambique (MOZ) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Malaysia (MYS) = ± s min = City population, log s C i t y r an k , l o g r Kuala Lumpur
Singapore
Bukit Mertajam
Ipoh
Kota Kinabalu
George Town
Kuching
Melaka City
Kota Bharu
Malaysia (MYS) = ± s min = City population, log s C i t y G D P , l o g y Kuala Lumpur
Singapore
Bukit Mertajam
Ipoh
Kota Kinabalu
George Town
Kuching
Melaka City
Kota Bharu
Malaysia (MYS) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Niger (NER) = ± s min = City population, log s C i t y r an k , l o g r Niamey
Tahoua
Zinder
Maradi
Dosso
Birni N'Konni
Gaya
Tillabéri
Dogondoutchi
Tessaoua
Madaoua
Tanout
Diffa
Magaria
Galmi
Agadez
Baléyara
Filingué
Gazaoua
Tchadoua
Keïta
Aguié
Niger (NER) = ± s min = City population, log s C i t y G D P , l o g y Niamey
Tahoua
Zinder
Maradi
Dosso
Birni N'Konni
Gaya
Tillabéri
Dogondoutchi
Tessaoua
Madaoua
Tanout
Diffa
Magaria
Galmi
Agadez
Baléyara
Filingué
Gazaoua
Tchadoua
Keïta
Aguié
Niger (NER) = ± .0 5.5 6.0 6.5 7.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Nigeria (NGA) = ± s min = City population, log s C i t y r an k , l o g r Lagos
Kano
Onitsha
Ibadan
Amaigbo
Abuja
Kaduna
Benin City
Port Harcourt
Oboama Nguru
Aba
Ilorin
Enugu
Maiduguri
Jos
Warri
Uyo
Osogbo
Zaria
Okene
Ikorodu
Sokoto
Abeokuta
Jimeta
Calabar
Akure
Katsina
Oyo
Bauchi
Igbe
Yenagoa
Ado Ekiti
Ondo
Minna
Ilesa
Gboko
Nsukka
Umuahia
Daura
Ife
Ogbomosho
Sapele
Ijebu-Ode
Makurdi
Kafanchan
Saki
Gombe
Gusau
Gwagwalada
Ijebu-Igbo
Potiskum
Mubi
Oron
Iragbiji
Abakaliki
Mogho
Bida
Krakrama
Iseyin
Obudu
Jalingo
Lafia
Otukpo
Owo
Birnin Kebbi
Bonny
Gamboru
Jega
Ikire
Iwo
Azare
Wukari
Dutse
Ise
Bugama
Funtua
Ughelli
Damboa
Zaki Biam
Lokoja
Katsina Ala
Biu
Biliri
Eket
Vande Ikya
Auchi
Sagamu
Gwoza
Gubio
Ankpa
Geidam
Hadejia
Jaudiri
Sangasumi
Zuru
Omuo-Obadore
Masuri
Wudil
Gashua
Agbor
Ore
Ikot Ekpene
Lawmu Umunze
Ugep
Ikerre
Ijagbo Offa
Nguru
Iwere kazaure
Kaura-Namoda
Okuku Lepuole
Omenama
Oyigbo
Ediene
Ile Oluji
Ozizza
Goniri
Michika
Kontagora
Irri
Keffi
Misau
Okitipupa
Kishi
Ningi
Samunakar
Ikom
Zinna
Kaltungo
Ugbokolo
Umu Lawlaw
Ekpoma
Tuga Nama
Malumfashi
Ayangba
Bajoga
Ebute Irele
Bori
Mongu Arna
Umundi
Dikwa
Takum
Ikole
Otun
Ijero-Ekiti
Baga
Uromi
Damagum
Omoko
Gembu
Ejigbo
Igboho
Idah
Onne
Enugu-Ezike
Dambarta
Uduagba
Dengi
Enwan
Aramoko-Ekiti
Ishiagu
Epe
Omema
Tarzoho
Langtang
New Bussa
Katsiro
Koko
Doka Ashafa
Gumel
Bichi
Elu
Nassarawan Eggon
Argungu
Akwanga
Shema
Gombi
Nshebori
Birnin Kudu
Gwarzo
Doma
Song
Gummi
Alesa
Wurno
Ikot Akpanata
Mashi
Buni Yadi
Awala
Egbe
Damaturu
Monguno
Eruwa Titun
Tudun Wada
Biantubu
Agaie
Gamawa
Shendam
Shellem
Numan
Giade
Effon Alaiye
Kpam
Jahun
Dukku
Gaya
Awgu
Maya Belwa
Ekogboro
Igbo Ora
Ilaro
Bununu Dass
Adikpo
Ido Ekiti
Idanre
Owode
Donga
Igbeti
Kamba
Ilawe-Ekiti
Amaba
Koi
Bokkos
Imorun
Ikolo
Damask
Jemmaare
Obinomba
Tudun Wada
Gulak
Kabba
Bagudo
Isa
Dundewa
Abiriba
UNNAMED
Mafara
Uba
Ogwashi Uku
Damban
Bunza
Jakusko
Idembia
Maigatari
Rano
Nigeria (NGA) = ± s min = City population, log s C i t y G D P , l o g y Lagos
Kano
Onitsha
Ibadan
Amaigbo
Abuja
Kaduna
Benin City
Port Harcourt
Oboama Nguru
Aba
Ilorin
Enugu
Maiduguri
Jos
Warri
Uyo
Osogbo
Zaria
Okene
Ikorodu
Sokoto
Abeokuta
Jimeta
Calabar
Akure
Katsina
Oyo
Bauchi
Igbe
Yenagoa
Ado Ekiti
Ondo
Minna
Ilesa
Gboko
Nsukka
Umuahia
Daura
Ife
Ogbomosho
Sapele
Ijebu-Ode
Makurdi
Kafanchan
Saki
Gombe
Gusau
Gwagwalada
Ijebu-Igbo
Potiskum
Mubi
Oron
Iragbiji
Abakaliki
Mogho
Bida
Krakrama
Iseyin
Obudu
Jalingo
Lafia
Otukpo
Owo
Birnin Kebbi
Bonny
Gamboru
Jega
Ikire
Iwo
Azare
Wukari
Dutse
Ise
Bugama
Funtua
Ughelli
Damboa
Zaki Biam
Lokoja
Katsina Ala
Biu
Biliri
Eket
Vande Ikya
Auchi
Sagamu
Gwoza
Gubio
Ankpa
Geidam
Hadejia
Jaudiri
Sangasumi
Zuru
Omuo-Obadore
Masuri
Wudil
Gashua
Agbor
Ore
Ikot Ekpene
Lawmu Umunze
Ugep
Ikerre
Ijagbo Offa
Nguru
Iwere kazaure
Kaura-Namoda
Okuku Lepuole
Omenama
Oyigbo
Ediene
Ile Oluji
Ozizza
Goniri
Michika
Kontagora
Irri
Keffi
Misau
Okitipupa
Kishi
Ningi
Samunakar
Ikom
Zinna
Kaltungo
Ugbokolo
Umu Lawlaw
Ekpoma
Tuga Nama
Malumfashi
Ayangba
Bajoga
Ebute Irele
Bori
Mongu Arna
Umundi
Dikwa
Takum
Ikole
Otun
Ijero-Ekiti
Baga
Uromi
Damagum
Omoko
Gembu
Ejigbo
Igboho
Idah
Onne
Enugu-Ezike
Dambarta
Uduagba
Dengi
Enwan
Aramoko-Ekiti
Ishiagu
Epe
Omema
Tarzoho
Langtang
New Bussa
Katsiro
Koko
Doka Ashafa
Gumel
Bichi
Elu
Nassarawan Eggon
Argungu
Akwanga
Shema
Gombi
Nshebori
Birnin Kudu
Gwarzo
Doma
Song
Gummi
Alesa
Wurno
Ikot Akpanata
Mashi
Buni Yadi
Awala
Egbe
Damaturu
Monguno
Eruwa Titun
Tudun Wada
Biantubu
Agaie
Gamawa
Shendam
Shellem
Numan
Giade
Effon Alaiye
Kpam
Jahun
Dukku
Gaya
Awgu
Maya Belwa
Ekogboro
Igbo Ora
Ilaro
Bununu Dass
Adikpo
Ido Ekiti
Idanre
Owode
Donga
Igbeti
Kamba
Ilawe-Ekiti
Amaba
Koi
Bokkos
Imorun
Ikolo
Damask
Jemmaare
Obinomba
Tudun Wada
Gulak
Kabba
Bagudo
Isa
Dundewa
Abiriba
UNNAMED
Mafara
Uba
Ogwashi Uku
Damban
Bunza
Jakusko
Idembia
Maigatari
Rano
Nigeria (NGA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Nicaragua (NIC) = ± s min = City population, log s C i t y r an k , l o g r Managua
León
Chinandega
Masaya
Matagalpa
Esteli
Jinotepe
Jinotega
Nicaragua (NIC) = ± s min = City population, log s C i t y G D P , l o g y Managua
León
Chinandega
Masaya
Matagalpa
Esteli
Jinotepe
Jinotega
Nicaragua (NIC) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Netherlands (NLD) = ± s min = City population, log s C i t y r an k , l o g r Rotterdam [The Hague]
Amsterdam
Arnhem
Utrecht
Eindhoven
Enschede 's-Hertogenbosch
Amersfoort
Tilburg
Groningen
Breda
Maastricht
Zwolle
Alkmaar
Veenendaal
Heerlen
Almere
Hilversum
Venlo
Roosendaal
Apeldoorn
Netherlands (NLD) = ± s min = City population, log s C i t y G D P , l o g y Rotterdam [The Hague]
Amsterdam
Arnhem
Utrecht
Eindhoven
Enschede 's-Hertogenbosch
Amersfoort
Tilburg
Groningen
Breda
Maastricht
Zwolle
Alkmaar
Veenendaal
Heerlen
Almere
Hilversum
Venlo
Roosendaal
Apeldoorn
Netherlands (NLD) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Nepal (NPL) = ± s min = City population, log s C i t y r an k , l o g r Kathmandu
Itahari
Pokhariya
Pokhara
Bharatpur
Nepalgunj
Hetauda
Damak
Tilottama
Birtamod
Nepal (NPL) = ± s min = City population, log s C i t y G D P , l o g y Kathmandu
Itahari
Pokhariya
Pokhara
Bharatpur
Nepalgunj
Hetauda
Damak
Tilottama
Birtamod
Nepal (NPL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Oman (OMN) = ± s min = City population, log s C i t y r an k , l o g r Al Ghubra
Seeb
Salalah
Sohar
Ibri
Nizwa
Balad Bani Bu Ali
Al Ain
Al Amerat
Oman (OMN) = ± s min = City population, log s C i t y G D P , l o g y Al Ghubra
Seeb
Salalah
Sohar
Ibri
Nizwa
Balad Bani Bu Ali
Al Ain
Al Amerat
Oman (OMN) = ± .0 5.5 6.0 6.5 7.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Pakistan (PAK) = ± s min = City population, log s C i t y r an k , l o g r Karachi
Lahore
Peshawar
Faisalabad
Rawalpindi [Islamabad]
Gujranwala
Multan
Sialkot
Hyderabad
Abbottabad
Mardan
Swat City
Gujrat
Quetta
Sargodha
Wah Cantonment
Bannu
Okara
Kasur
Haripur
Bahawalpur
Jhelum
Larkana
Sukkur
Sahiwal
Mirpur Khas
Kamra
Chakdara
Dera Ghazi Khan
Kharian
Pattoki
Tando Allayhar
Kohat
Swabi
Badin
Chakwal
Rahimyar Khan
Shakar Garh
Jhang
Narowal
Muzaffarabad
Takht-e-Bhai
Jampur
Muzaffargarh
Jacobabad
Mandi Bahauddin
Hafizabad
Burewala
Timergara
Sadiqabad
Shikarpur
Khatako Shah
Tando Adam
Chiniot
Panjgur
Chunian
Shahdadkot
UNNAMED
Kotli
Khairpur
Daharki
Khuzdar
Rana Khemraj
Turbat
Hangu
Pakpattan
Shahdadpur
Gojra
Sangla Hill
Dadu
Khwazakhela
Dera Ismail Khan
Tarakai
Bindi
Munda
Sowari
Lodhran
Kandhkot
Tando Muhammad Khan
Battagram
Khanewal
Pasrur
Shujaabad
Munda Qala
Fateh Jang
Alipur
Pindi Gheb
Mangowal
Arifwala
Layyah
Topi
Thul
Khanpur
Kabirwala
Hasilpur
Usta Muhammad
Kahuta
Nawabshah
Havelian
Dir
Moro
Pir Murad
Dina
Toba Tek Singh
Ahmadpur East
Balakot
Dera Murad Jamali
Attock
Kahror Pakka
Mithankot
Pakistan (PAK) = ± s min = City population, log s C i t y G D P , l o g y Karachi
Lahore
Peshawar
Faisalabad
Rawalpindi [Islamabad]
Gujranwala
Multan
Sialkot
Hyderabad
Abbottabad
Mardan
Swat City
Gujrat
Quetta
Sargodha
Wah Cantonment
Bannu
Okara
Kasur
Haripur
Bahawalpur
Jhelum
Larkana
Sukkur
Sahiwal
Mirpur Khas
Kamra
Chakdara
Dera Ghazi Khan
Kharian
Pattoki
Tando Allayhar
Kohat
Swabi
Badin
Chakwal
Rahimyar Khan
Shakar Garh
Jhang
Narowal
Muzaffarabad
Takht-e-Bhai
Jampur
Muzaffargarh
Jacobabad
Mandi Bahauddin
Hafizabad
Burewala
Timergara
Sadiqabad
Shikarpur
Khatako Shah
Tando Adam
Chiniot
Panjgur
Chunian
Shahdadkot
UNNAMED
Kotli
Khairpur
Daharki
Khuzdar
Rana Khemraj
Turbat
Hangu
Pakpattan
Shahdadpur
Gojra
Sangla Hill
Dadu
Khwazakhela
Dera Ismail Khan
Tarakai
Bindi
Munda
Sowari
Lodhran
Kandhkot
Tando Muhammad Khan
Battagram
Khanewal
Pasrur
Shujaabad
Munda Qala
Fateh Jang
Alipur
Pindi Gheb
Mangowal
Arifwala
Layyah
Topi
Thul
Khanpur
Kabirwala
Hasilpur
Usta Muhammad
Kahuta
Nawabshah
Havelian
Dir
Moro
Pir Murad
Dina
Toba Tek Singh
Ahmadpur East
Balakot
Dera Murad Jamali
Attock
Kahror Pakka
Mithankot
Pakistan (PAK) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Peru (PER) = ± s min = City population, log s C i t y r an k , l o g r Lima
Trujillo
Arequipa
Chiclayo
Piura
Cusco
Huancayo
Pucallpa
Chimbote
Tacna
Juliaca
Peru (PER) = ± s min = City population, log s C i t y G D P , l o g y Lima
Trujillo
Arequipa
Chiclayo
Piura
Cusco
Huancayo
Pucallpa
Chimbote
Tacna
Juliaca
Peru (PER) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Philippines (PHL) = ± s min = City population, log s C i t y r an k , l o g r Quezon City [Manila]
Cebu City
Angeles [San Fernando]
Davao City
Dagupan
Cagayan de Oro
Iloilo City
Bacolod
Baguio
Zamboanga City
Batangas City
General Santos
Naga
Tarlac City
Iligan
Cabanatuan
Olongapo
Lucena
Tacloban
Tagum
Cotabato
Legazpi
Marawi
Balanga
Butuan
Dumaguete
San Fernando
Gapan
Puerto Princesa
Urdaneta
Pagadian
Tuguegarao
Tagbilaran
Ozamiz
Dipolog
Roxas City
Tabaco
Lemery
Koronadal
Kalibo
Vigan
Digos
Santiago
Ormoc
Bayambang
Panabo
Jolo
Daet
San Jose
Laoag
Surigao City
Sorsogon City
Valencia
Bayombong
Puray
Calbayog
Isabela City
Iriga
Candelaria
Calapan
Philippines (PHL) = ± s min = City population, log s C i t y G D P , l o g y Quezon City [Manila]
Cebu City
Angeles [San Fernando]
Davao City
Dagupan
Cagayan de Oro
Iloilo City
Bacolod
Baguio
Zamboanga City
Batangas City
General Santos
Naga
Tarlac City
Iligan
Cabanatuan
Olongapo
Lucena
Tacloban
Tagum
Cotabato
Legazpi
Marawi
Balanga
Butuan
Dumaguete
San Fernando
Gapan
Puerto Princesa
Urdaneta
Pagadian
Tuguegarao
Tagbilaran
Ozamiz
Dipolog
Roxas City
Tabaco
Lemery
Koronadal
Kalibo
Vigan
Digos
Santiago
Ormoc
Bayambang
Panabo
Jolo
Daet
San Jose
Laoag
Surigao City
Sorsogon City
Valencia
Bayombong
Puray
Calbayog
Isabela City
Iriga
Candelaria
Calapan
Philippines (PHL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Poland (POL) = ± s min = City population, log s C i t y r an k , l o g r Katowice
Warsaw
Krakow
Lodz
Gdansk
Poznan
Wroclaw
Lublin
Rybnik
Bielsko-Biaa
Bydgoszcz
Szczecin
Cz stochowa
Rzeszów
Biaystok
Kielce
Toru
Radom
Wabrzych
Nowy Scz
Opole
Olsztyn
Pock
Kalisz
Gorzów Wielkopolski
Jelenia Góra
Koszalin
Inowrocaw
Legnica
Wejherowo
Ostrowiec witokrzyski
Ostrów Wielkopolski widnica
Gniezno
Lubin
Gronowo Górne
Tomaszów Mazowiecki
Tczew
Leszno
Pia
Poland (POL) = ± s min = City population, log s C i t y G D P , l o g y Katowice
Warsaw
Krakow
Lodz
Gdansk
Poznan
Wroclaw
Lublin
Rybnik
Bielsko-Biaa
Bydgoszcz
Szczecin
Cz stochowa
Rzeszów
Biaystok
Kielce
Toru
Radom
Wabrzych
Nowy Scz
Opole
Olsztyn
Pock
Kalisz
Gorzów Wielkopolski
Jelenia Góra
Koszalin
Inowrocaw
Legnica
Wejherowo
Ostrowiec witokrzyski
Ostrów Wielkopolski widnica
Gniezno
Lubin
Gronowo Górne
Tomaszów Mazowiecki
Tczew
Leszno
Pia
Poland (POL) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) North Korea (PRK) = ± s min = City population, log s C i t y r an k , l o g r Pyongyang
Hamhung
Ch ngjin
Sariw n
Wonsan
P'y ngs ng
Dandong
Nampo
Anju
Kanggye
Haeju
Songnim
Kaesong
Kimch'aek
Hyesan
Huichon
Sillyeonpo
Jongju
Kaechon
Tokchon
Sinchon
Ryongchon
Munchon
Hongwon
Omong-ri
Sinpyong
Sonchon
Rason
Musan
Koksan
Jongphyong
Kusong
Phyongwon
Sukchon
Hamju
Anak
Kujang
Jaeryong
Kumya
Jonchon
Sinpho
Kangdong
Tongrim
Hoeryong
UNNAMED
Yonan
Unchon
Chongnam
Ji'an
Tktaedonggok
Taean
Kosan
Kowon
Hoechang
Chonnae
North Korea (PRK) = ± s min = City population, log s C i t y G D P , l o g y Pyongyang
Hamhung
Ch ngjin
Sariw n
Wonsan
P'y ngs ng
Dandong
Nampo
Anju
Kanggye
Haeju
Songnim
Kaesong
Kimch'aek
Hyesan
Huichon
Sillyeonpo
Jongju
Kaechon
Tokchon
Sinchon
Ryongchon
Munchon
Hongwon
Omong-ri
Sinpyong
Sonchon
Rason
Musan
Koksan
Jongphyong
Kusong
Phyongwon
Sukchon
Hamju
Anak
Kujang
Jaeryong
Kumya
Jonchon
Sinpho
Kangdong
Tongrim
Hoeryong
UNNAMED
Yonan
Unchon
Chongnam
Ji'an
Tktaedonggok
Taean
Kosan
Kowon
Hoechang
Chonnae
North Korea (PRK) = ± .25 5.50 5.75 6.00 6.25 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Romania (ROU) = ± s min = City population, log s C i t y r an k , l o g r Bucharest
C l ra i
Cluj-Napoca
Timi oara
Constana
Ia i
Brasov
Ploie ti
Craiova
Galai
Oradea
Pite ti
Târgu Mure
Bac u
Arad
Br ila
Sibiu
Baia Mare
Oltenia
Buzu
Romania (ROU) = ± s min = City population, log s C i t y G D P , l o g y Bucharest
C l ra i
Cluj-Napoca
Timi oara
Constana
Ia i
Brasov
Ploie ti
Craiova
Galai
Oradea
Pite ti
Târgu Mure
Bac u
Arad
Br ila
Sibiu
Baia Mare
Oltenia
Buzu
Romania (ROU) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Russia (RUS) = ± s min = City population, log s C i t y r an k , l o g r Moscow
Saint Petersburg
Novosibirsk
Yekaterinburg
Volgograd
Nizhny Novgorod
Rostov-on-Don
Chelyabinsk
Samara
Kazan
Omsk
Voronezh
Ufa
Saratov
Krasnoyarsk
Krasnodar
Makhachkala
Tolyatti
Vladivostok
Barnaul
Tyumen
Tomsk
Irkutsk
Ulyanovsk
Izhevsk
Astrakhan
Penza
Yaroslavl
Khabarovsk
Orenburg
Naberezhnye Chelny
Tula
Kemerovo
Lipetsk
Ryazan
Stavropol
Novokuznetsk
Kaliningrad
Cheboksary
Bryansk
Kirov
Ivanovo
Belgorod
Ulan-Ude
Russia (RUS) = ± s min = City population, log s C i t y G D P , l o g y Moscow
Saint Petersburg
Novosibirsk
Yekaterinburg
Volgograd
Nizhny Novgorod
Rostov-on-Don
Chelyabinsk
Samara
Kazan
Omsk
Voronezh
Ufa
Saratov
Krasnoyarsk
Krasnodar
Makhachkala
Tolyatti
Vladivostok
Barnaul
Tyumen
Tomsk
Irkutsk
Ulyanovsk
Izhevsk
Astrakhan
Penza
Yaroslavl
Khabarovsk
Orenburg
Naberezhnye Chelny
Tula
Kemerovo
Lipetsk
Ryazan
Stavropol
Novokuznetsk
Kaliningrad
Cheboksary
Bryansk
Kirov
Ivanovo
Belgorod
Ulan-Ude
Russia (RUS) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Saudi Arabia (SAU) = ± s min = City population, log s C i t y r an k , l o g r Riyadh
Jeddah
Dammam
Mecca
Medina
Hofuf
At Taif
Khamis Mushait
Tabuk
Al Jubayl Industrial City
Buraydah
Unaizah
Hail
Hafar Al-Batin
Al-Kharj
Najran
Al Hawiyah
Abha
Arar
Sakaka
Sabya
Abu Arish
Muhayil
Madnat Yanbu a in yah
Al Qurayyat
Saudi Arabia (SAU) = ± s min = City population, log s C i t y G D P , l o g y Riyadh
Jeddah
Dammam
Mecca
Medina
Hofuf
At Taif
Khamis Mushait
Tabuk
Al Jubayl Industrial City
Buraydah
Unaizah
Hail
Hafar Al-Batin
Al-Kharj
Najran
Al Hawiyah
Abha
Arar
Sakaka
Sabya
Abu Arish
Muhayil
Madnat Yanbu a in yah
Al Qurayyat
Saudi Arabia (SAU) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Sudan (SDN) = ± s min = City population, log s C i t y r an k , l o g r Khartoum
Nyala
Al-Ubayyid
Al-Fashir
Buram
Port Sudan
Wad Madan
Ad Da'ein
Al Managil
Al Hasahisa
Kosti
Umm Ruwaba
Kas
Kassala
Al-Qadarif
En Nahud
Ad-Damazin
Saraf `Umrah
Giad Industrial Complex
Geneina
Barah
Al Rahad
Rabak
Shendi
Atbara
UNNAMED
Ghubaysh
Jebel Aulia
Sennar
Abu Jibeha
Tandalti
Mellit ad-Damer
Al Hilaliyah
Al Quwaysi
Ed Dueim
Dilling
UNNAMED
New Halfa
UNNAMED
UNNAMED
Muglad
Sudan (SDN) = ± s min = City population, log s C i t y G D P , l o g y Khartoum
Nyala
Al-Ubayyid
Al-Fashir
Buram
Port Sudan
Wad Madan
Ad Da'ein
Al Managil
Al Hasahisa
Kosti
Umm Ruwaba
Kas
Kassala
Al-Qadarif
En Nahud
Ad-Damazin
Saraf `Umrah
Giad Industrial Complex
Geneina
Barah
Al Rahad
Rabak
Shendi
Atbara
UNNAMED
Ghubaysh
Jebel Aulia
Sennar
Abu Jibeha
Tandalti
Mellit ad-Damer
Al Hilaliyah
Al Quwaysi
Ed Dueim
Dilling
UNNAMED
New Halfa
UNNAMED
UNNAMED
Muglad
Sudan (SDN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Senegal (SEN) = ± s min = City population, log s C i t y r an k , l o g r Dakar
Touba
MBour
Thiès
Kaolack
Diourbel
Tambacounda
Kolda
Ziguinchor
Kaffrine
Saint-Louis
Louga
Koungheul
Dahra Djoloff
Vélingara
Bambey
Fatick
Sédhiou
Madina Gounass
Kedougou
Richard-Toll
Bignona
Gossas
Tivaouane
Dagana
Goudomp
Guinguinéo
Senegal (SEN) = ± s min = City population, log s C i t y G D P , l o g y Dakar
Touba
MBour
Thiès
Kaolack
Diourbel
Tambacounda
Kolda
Ziguinchor
Kaffrine
Saint-Louis
Louga
Koungheul
Dahra Djoloff
Vélingara
Bambey
Fatick
Sédhiou
Madina Gounass
Kedougou
Richard-Toll
Bignona
Gossas
Tivaouane
Dagana
Goudomp
Guinguinéo
Senegal (SEN) = ± .00 5.25 5.50 5.75 6.00 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Somalia (SOM) = ± s min = City population, log s C i t y r an k , l o g r Mogadishu
Hargeisa
Baidoa
Burao
Borama
Bosaso
Kismayo
Xawo Tako
Galkayo
Buurhakaba
Merca
Erigavo
Qardho City
Beledweyne
Las Anod
Dhuusamareeb
Dara Salaam
Garoowe
Berbera
Somalia (SOM) = ± s min = City population, log s C i t y G D P , l o g y Mogadishu
Hargeisa
Baidoa
Burao
Borama
Bosaso
Kismayo
Xawo Tako
Galkayo
Buurhakaba
Merca
Erigavo
Qardho City
Beledweyne
Las Anod
Dhuusamareeb
Dara Salaam
Garoowe
Berbera
Somalia (SOM) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Serbia (SRB) = ± s min = City population, log s C i t y r an k , l o g r Belgrade
Novi Sad Ni Kragujevac
Subotica
Serbia (SRB) = ± s min = City population, log s C i t y G D P , l o g y Belgrade
Novi Sad Ni Kragujevac
Subotica
Serbia (SRB) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) South Sudan (SSD) = ± s min = City population, log s C i t y r an k , l o g r Juba
Nimule
Torit
Yei
Bor
Wau
Kuajok
Rumbek
Renk
Yambio
Malakal
Aweil
South Sudan (SSD) = ± s min = City population, log s C i t y G D P , l o g y Juba
Nimule
Torit
Yei
Bor
Wau
Kuajok
Rumbek
Renk
Yambio
Malakal
Aweil
South Sudan (SSD) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Sweden (SWE) = ± s min = City population, log s C i t y r an k , l o g r Stockholm
Gothenburg
Malmö
Helsingborg
Uppsala
Lund
Örebro
Västerås
Linköping
Sweden (SWE) = ± s min = City population, log s C i t y G D P , l o g y Stockholm
Gothenburg
Malmö
Helsingborg
Uppsala
Lund
Örebro
Västerås
Linköping
Sweden (SWE) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Syria (SYR) = ± s min = City population, log s C i t y r an k , l o g r Damascus
Aleppo
Homs
Latakia
Hama
Al-Hasakah
Qamishli
Ar Raqqah
Deir Ez Zor
Manbij
Tartus
Al Qurayya
Bza`a
Idlib
Jablah
As Suwayda
Baniyas
Al-Tabqah
As Safirah `Uthman
Kobani
Abu Kamal
Syria (SYR) = ± s min = City population, log s C i t y G D P , l o g y Damascus
Aleppo
Homs
Latakia
Hama
Al-Hasakah
Qamishli
Ar Raqqah
Deir Ez Zor
Manbij
Tartus
Al Qurayya
Bza`a
Idlib
Jablah
As Suwayda
Baniyas
Al-Tabqah
As Safirah `Uthman
Kobani
Abu Kamal
Syria (SYR) = ± .4 5.6 5.8 6.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Chad (TCD) = ± s min = City population, log s C i t y r an k , l o g r N'Djamena
Abéché
Moundou
Pala
Sarh
Adré
Fianga
Koumra
Ati
Mongo
Bongor
Umm Hajar
Laï
Doba
Mao
Chad (TCD) = ± s min = City population, log s C i t y G D P , l o g y N'Djamena
Abéché
Moundou
Pala
Sarh
Adré
Fianga
Koumra
Ati
Mongo
Bongor
Umm Hajar
Laï
Doba
Mao
Chad (TCD) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Togo (TGO) = ± s min = City population, log s C i t y r an k , l o g r Lomé
Kara
Sokodé
Atakpamé
Dapaong
Sansanné-Mango
Kpalimé
Anié
Blitta-Gare
Tsévié
Tchamba
Notsé
Togo (TGO) = ± s min = City population, log s C i t y G D P , l o g y Lomé
Kara
Sokodé
Atakpamé
Dapaong
Sansanné-Mango
Kpalimé
Anié
Blitta-Gare
Tsévié
Tchamba
Notsé
Togo (TGO) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Thailand (THA) = ± s min = City population, log s C i t y r an k , l o g r Bangkok
Chiang Mai
Chonburi
Phuket
Hat Yai
Rayong
Nakhon Pathom
Nakhon Ratchasima
Pattaya
Khon Kaen
Laem Chabang
Phitsanulok
Songkhla
Nakhon Si Thammarat
Surat Thani
Udon Thani
Lopburi
Phra Nakhon Si Ayutthaya
Lampang
Ubon Ratchathani
Thailand (THA) = ± s min = City population, log s C i t y G D P , l o g y Bangkok
Chiang Mai
Chonburi
Phuket
Hat Yai
Rayong
Nakhon Pathom
Nakhon Ratchasima
Pattaya
Khon Kaen
Laem Chabang
Phitsanulok
Songkhla
Nakhon Si Thammarat
Surat Thani
Udon Thani
Lopburi
Phra Nakhon Si Ayutthaya
Lampang
Ubon Ratchathani
Thailand (THA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Tajikistan (TJK) = ± s min = City population, log s C i t y r an k , l o g r Dushanbe
Khujand
Kulob
Hisor
Vahdat
UNNAMED
Proletar
Isfara
Khistevarz
Qabodiyon
Tajikistan (TJK) = ± s min = City population, log s C i t y G D P , l o g y Dushanbe
Khujand
Kulob
Hisor
Vahdat
UNNAMED
Proletar
Isfara
Khistevarz
Qabodiyon
Tajikistan (TJK) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Turkmenistan (TKM) = ± s min = City population, log s C i t y r an k , l o g r Ashgabat
Mary
Dashoguz
Turkmenabat
Garada aýak
Turkmenistan (TKM) = ± s min = City population, log s C i t y G D P , l o g y Ashgabat
Mary
Dashoguz
Turkmenabat
Garada aýak
Turkmenistan (TKM) = ± .0 5.5 6.0 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Tunisia (TUN) = ± s min = City population, log s C i t y r an k , l o g r Tunis
Sfax
Sousse
Hammamet
Bizerte
Gabes
Ksar Hellal
Qafsa
Medenine
Tunisia (TUN) = ± s min = City population, log s C i t y G D P , l o g y Tunis
Sfax
Sousse
Hammamet
Bizerte
Gabes
Ksar Hellal
Qafsa
Medenine
Tunisia (TUN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Turkey (TUR) = ± s min = City population, log s C i t y r an k , l o g r Istanbul
Ankara
Izmir
Bursa
Gaziantep
Sincan
Antalya
Konya
Mersin zmit
Kayseri
Adana
Diyarbakir
Samsun
Denizli
Eskisehir
Kahramanmara
Malatya anlurfa
Antakya
Van
Trabzon
Sakarya [Adapazar]
Batman
Elazig
Sivas
Manisa skenderun
Kapakl
Balkesir
Isparta
Aydin
Osmaniye
Düzce
Adiyaman
Ordu
Tarsus
Çorum
Afyonkarahisar negöl
Günyurdu
Zonguldak
Arnavutköy
Karabük
Kütahya
Siverek
Uak
Giresun
Aksaray
Yalova
Turgutlu
Tokat
Fethiye
Erzurum
Siirt
Ereli
Yumurtalk
Rize
Bolu
Karaman Ar Erci
Silivri
Alanya
Silopi
Çanakkale
Çorlu
Ceyhan
Keskin
Kadirli
Kastamonu
Tekirda Mu Nide
Viranehir
Samanda
Manavgat
Elbistan
Cizre
Bingöl
Eregli
Turkey (TUR) = ± s min = City population, log s C i t y G D P , l o g y Istanbul
Ankara
Izmir
Bursa
Gaziantep
Sincan
Antalya
Konya
Mersin zmit
Kayseri
Adana
Diyarbakir
Samsun
Denizli
Eskisehir
Kahramanmara
Malatya anlurfa
Antakya
Van
Trabzon
Sakarya [Adapazar]
Batman
Elazig
Sivas
Manisa skenderun
Kapakl
Balkesir
Isparta
Aydin
Osmaniye
Düzce
Adiyaman
Ordu
Tarsus
Çorum
Afyonkarahisar negöl
Günyurdu
Zonguldak
Arnavutköy
Karabük
Kütahya
Siverek
Uak
Giresun
Aksaray
Yalova
Turgutlu
Tokat
Fethiye
Erzurum
Siirt
Ereli
Yumurtalk
Rize
Bolu
Karaman Ar Erci
Silivri
Alanya
Silopi
Çanakkale
Çorlu
Ceyhan
Keskin
Kadirli
Kastamonu
Tekirda Mu Nide
Viranehir
Samanda
Manavgat
Elbistan
Cizre
Bingöl
Eregli
Turkey (TUR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Taiwan (TWN) = ± s min = City population, log s C i t y r an k , l o g r New Taipei [Taipei]
Taichung
Kaohsiung
Tainan
Hsinchu
Chiayi
Luodong
Hualien
Miaoli
Xinying District
Taiwan (TWN) = ± s min = City population, log s C i t y G D P , l o g y New Taipei [Taipei]
Taichung
Kaohsiung
Tainan
Hsinchu
Chiayi
Luodong
Hualien
Miaoli
Xinying District
Taiwan (TWN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Tanzania (TZA) = ± s min = City population, log s C i t y r an k , l o g r Dar es Salaam
Mwanza
Zanzibar City
Arusha
Mbeya
Morogoro
Kilima Hewa
Dodoma
Tanga
Moshi
Songea
Tabora
Musoma
Sumbawanga
Bukoba
Shinyanga
Kahama
Geita
Katoro
Ndiuka
Tunduma
Murubona
Mtwara
Mpanda
Iwambi
Ifakara
Bukala
Singida
Tanzania (TZA) = ± s min = City population, log s C i t y G D P , l o g y Dar es Salaam
Mwanza
Zanzibar City
Arusha
Mbeya
Morogoro
Kilima Hewa
Dodoma
Tanga
Moshi
Songea
Tabora
Musoma
Sumbawanga
Bukoba
Shinyanga
Kahama
Geita
Katoro
Ndiuka
Tunduma
Murubona
Mtwara
Mpanda
Iwambi
Ifakara
Bukala
Singida
Tanzania (TZA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Uganda (UGA) = ± s min = City population, log s C i t y r an k , l o g r Kampala
Jinja
Arua
Iganga
Gulu
Mbarara
Lira
Masaka
Mbale
Koboko
Kasese
Lugazi
Busia
Fort Portal
Mubende
Opuyo
Hoima
Busesa
Uganda (UGA) = ± s min = City population, log s C i t y G D P , l o g y Kampala
Jinja
Arua
Iganga
Gulu
Mbarara
Lira
Masaka
Mbale
Koboko
Kasese
Lugazi
Busia
Fort Portal
Mubende
Opuyo
Hoima
Busesa
Uganda (UGA) = ± .50 5.75 6.00 6.25 6.50 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Ukraine (UKR) = ± s min = City population, log s C i t y r an k , l o g r Kyiv
Kharkiv
Donetsk
Odesa
Dnipro
Lviv
Zaporizhzhia
Kryvyi Rih
Mykolaiv
Luhansk
Mariupol
Simferopol
Vinnytsia
Chernivtsi
Ivano-Frankivsk
Kherson
Poltava
Rivne
Sevastopol
Zhytomyr
Cherkasy
Chernihiv
Sievierodonetsk
Sumy
Khmelnytskyi
Kamianske
Kremenchuk
Lutsk
Horlivka
Ternopil
Ukraine (UKR) = ± s min = City population, log s C i t y G D P , l o g y Kyiv
Kharkiv
Donetsk
Odesa
Dnipro
Lviv
Zaporizhzhia
Kryvyi Rih
Mykolaiv
Luhansk
Mariupol
Simferopol
Vinnytsia
Chernivtsi
Ivano-Frankivsk
Kherson
Poltava
Rivne
Sevastopol
Zhytomyr
Cherkasy
Chernihiv
Sievierodonetsk
Sumy
Khmelnytskyi
Kamianske
Kremenchuk
Lutsk
Horlivka
Ternopil
Ukraine (UKR) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) United States (USA) = ± s min = City population, log s C i t y r an k , l o g r New York
Los Angeles
Chicago
Dallas
Houston
Philadelphia
Miami
Washington D.C.
Atlanta
San Jose
Phoenix
Detroit
Seattle
Minneapolis [Saint Paul]
Tijuana
Denver
Boston
Tampa
St. Louis
Orlando
Portland
Baltimore
Las Vegas
San Antonio
Sacramento
Charlotte
Pittsburgh
Kansas City
Cincinnati
Indianapolis
Austin
Columbus
Cleveland
Virginia Beach
Milwaukee
Raleigh
Providence
Louisville
Memphis
Oklahoma City
Salt Lake City
Jacksonville
Nashville
Bridgeport
Buffalo
Richmond
Hartford
Allentown
Tucson
Dayton
Honolulu
New Orleans
Ciudad Juárez
Albuquerque
Omaha
Concord
McAllen
Bradenton
Fresno
Rochester
Birmingham
Tulsa
Baton Rouge
Grand Rapids
Springfield
Greensboro
Albany
Bakersfield
Cape Coral
Colorado Springs
Harrisburg
Toledo
Akron
Columbia
Charleston
Ogden
Palm Bay
Waukegan
Provo
Knoxville
Syracuse
Des Moines
Lexington
South Bend
Madison
Wichita
Spokane
Lakeland
Worcester
Youngstown
Indio
Little Rock
Reading
Fort Wayne
Canton
Port St. Lucie
Winston-Salem
Reno
Temecula
Boise
Flint
Lancaster
Lansing
Salem
Modesto
Mobile
Oxnard
Rockford
Lafayette
Pensacola
Stockton
Lawrence
Fayetteville
Huntsville
Palmdale
Springfield
Brockton
Naples
Corpus Christi
York
Waterbury
Savannah
Davenport
Killeen
Shreveport
Hesperia
Santa Rosa
Port Arthur
Peoria
Kalamazoo
Ann Arbor
Visalia
Antioch
Eugene
Framingham
Montgomery
Lincoln
West Chester
Brownsville
Lubbock
Manchester
Daytona Beach
Tallahassee
Racine
Evansville
Columbus
Appleton
Anchorage
Saginaw
Nuevo Laredo
Portland
Santa Clarita
Hemet
Lowell
United States (USA) = ± s min = City population, log s C i t y G D P , l o g y New York
Los Angeles
Chicago
Dallas
Houston
Philadelphia
Miami
Washington D.C.
Atlanta
San Jose
Phoenix
Detroit
Seattle
Minneapolis [Saint Paul]
Tijuana
Denver
Boston
Tampa
St. Louis
Orlando
Portland
Baltimore
Las Vegas
San Antonio
Sacramento
Charlotte
Pittsburgh
Kansas City
Cincinnati
Indianapolis
Austin
Columbus
Cleveland
Virginia Beach
Milwaukee
Raleigh
Providence
Louisville
Memphis
Oklahoma City
Salt Lake City
Jacksonville
Nashville
Bridgeport
Buffalo
Richmond
Hartford
Allentown
Tucson
Dayton
Honolulu
New Orleans
Ciudad Juárez
Albuquerque
Omaha
Concord
McAllen
Bradenton
Fresno
Rochester
Birmingham
Tulsa
Baton Rouge
Grand Rapids
Springfield
Greensboro
Albany
Bakersfield
Cape Coral
Colorado Springs
Harrisburg
Toledo
Akron
Columbia
Charleston
Ogden
Palm Bay
Waukegan
Provo
Knoxville
Syracuse
Des Moines
Lexington
South Bend
Madison
Wichita
Spokane
Lakeland
Worcester
Youngstown
Indio
Little Rock
Reading
Fort Wayne
Canton
Port St. Lucie
Winston-Salem
Reno
Temecula
Boise
Flint
Lancaster
Lansing
Salem
Modesto
Mobile
Oxnard
Rockford
Lafayette
Pensacola
Stockton
Lawrence
Fayetteville
Huntsville
Palmdale
Springfield
Brockton
Naples
Corpus Christi
York
Waterbury
Savannah
Davenport
Killeen
Shreveport
Hesperia
Santa Rosa
Port Arthur
Peoria
Kalamazoo
Ann Arbor
Visalia
Antioch
Eugene
Framingham
Montgomery
Lincoln
West Chester
Brownsville
Lubbock
Manchester
Daytona Beach
Tallahassee
Racine
Evansville
Columbus
Appleton
Anchorage
Saginaw
Nuevo Laredo
Portland
Santa Clarita
Hemet
Lowell
United States (USA) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Uzbekistan (UZB) = ± s min = City population, log s C i t y r an k , l o g r Tashkent
Samarkand
Namangan
Qarshi
Fergana
Andijan
Jizzax
Kokand
Shahrisabz
Turtkul
Nukus
Katta-Kurgan
Urgench
Termez
Gijduvan
Denov
Bukhara
Khiva
Quva
Yangikurgan
Navoiy
Kosonsoy
Rishtan
Shahrixon
Altiarik
Hazorasp
Beruniy
Chirchiq
Uzun
Gulistan
Guzar
Koson
Yaypan
Urgut
Xonqa
Jarqurgon
Pakhtaobod
Buloqboshi
Chust
Sherobod
Gallaorol
Poytugh
Khujayli
Yozyovon
Uzbekistan (UZB) = ± s min = City population, log s C i t y G D P , l o g y Tashkent
Samarkand
Namangan
Qarshi
Fergana
Andijan
Jizzax
Kokand
Shahrisabz
Turtkul
Nukus
Katta-Kurgan
Urgench
Termez
Gijduvan
Denov
Bukhara
Khiva
Quva
Yangikurgan
Navoiy
Kosonsoy
Rishtan
Shahrixon
Altiarik
Hazorasp
Beruniy
Chirchiq
Uzun
Gulistan
Guzar
Koson
Yaypan
Urgut
Xonqa
Jarqurgon
Pakhtaobod
Buloqboshi
Chust
Sherobod
Gallaorol
Poytugh
Khujayli
Yozyovon
Uzbekistan (UZB) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Venezuela (VEN) = ± s min = City population, log s C i t y r an k , l o g r Caracas
Maracaibo
Valencia
Maracay
Barquisimeto
Barcelona
Ciudad Guayana
San Cristóbal
Maturin
Guarenas
Porlamar
Ciudad Bolívar
Cumana
Catia La Mar
Barinas
Mérida
Charallave
Cabimas
Acarigua
Santa Teresa del Tuy
Punto Fijo
Coro
Valera
Biruaca
Ciudad Ojeda
Venezuela (VEN) = ± s min = City population, log s C i t y G D P , l o g y Caracas
Maracaibo
Valencia
Maracay
Barquisimeto
Barcelona
Ciudad Guayana
San Cristóbal
Maturin
Guarenas
Porlamar
Ciudad Bolívar
Cumana
Catia La Mar
Barinas
Mérida
Charallave
Cabimas
Acarigua
Santa Teresa del Tuy
Punto Fijo
Coro
Valera
Biruaca
Ciudad Ojeda
Venezuela (VEN) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Vietnam (VNM) = ± s min = City population, log s C i t y r an k , l o g r Ho Chi Minh City
Hanoi
Long Xuyen
Haiphong
Nam nh à N ng
Can Tho
My Tho
Sa Dec City
Vung Tau
Nha Trang
Thanh Hóa
Hue
Vinh
Thái Nguyên
Tây Ninh
Quy Nh n
H i D ng
Phúc Th
Ha Long
Cai Ly
Qung Ngãi
Rch Giá
Buôn Ma Thu t
Phan Thiet
Phan Rang - Tháp Chàm
Bc Liêu i Ngha
Pleiku
Ca Mau
Sóc Trng
Ninh Bình
Dalat
Ph Lý
Tuy Hòa
Hip Ph c
Cao Lanh
Trà Vinh City
Vietnam (VNM) = ± s min = City population, log s C i t y G D P , l o g y Ho Chi Minh City
Hanoi
Long Xuyen
Haiphong
Nam nh à N ng
Can Tho
My Tho
Sa Dec City
Vung Tau
Nha Trang
Thanh Hóa
Hue
Vinh
Thái Nguyên
Tây Ninh
Quy Nh n
H i D ng
Phúc Th
Ha Long
Cai Ly
Qung Ngãi
Rch Giá
Buôn Ma Thu t
Phan Thiet
Phan Rang - Tháp Chàm
Bc Liêu i Ngha
Pleiku
Ca Mau
Sóc Trng
Ninh Bình
Dalat
Ph Lý
Tuy Hòa
Hip Ph c
Cao Lanh
Trà Vinh City
Vietnam (VNM) = ± .0 5.5 6.0 6.5 City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Yemen (YEM) = ± s min = City population, log s C i t y r an k , l o g r Sana'a
Ta'izz
Al Mansurah
Hodeidah
Ibb
Dhamar
Yarim
Al Mutadarririn
Sa'dah
Abs
Amran
Tarim
Seiyun
Harad
Lawdar
Shihr
Al Beidha
Rada'a
Al Milhi
Hajja
Al Qatn
Ad Dala
Yemen (YEM) = ± s min = City population, log s C i t y G D P , l o g y Sana'a
Ta'izz
Al Mansurah
Hodeidah
Ibb
Dhamar
Yarim
Al Mutadarririn
Sa'dah
Abs
Amran
Tarim
Seiyun
Harad
Lawdar
Shihr
Al Beidha
Rada'a
Al Milhi
Hajja
Al Qatn
Ad Dala
Yemen (YEM) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) South Africa (ZAF) = ± s min = City population, log s C i t y r an k , l o g r Johannesburg
Cape Town
Durban
Pretoria
Klipgat
Port Elizabeth
Evaton
Tsakane
Edendale
Bloemfontein
East London
Rustenburg
Polokwane
Osizweni
Vanderbijlpark eGobhoza
Phuthaditjhaba
Paarl
Kimberley
Somerset West
Emalahleni
Middelburg
Botshabelo
Mafikeng
George
Bronville
KwaMhlanga
Potchefstroom
Jouberton
Vosman eMbalenhle
Sasolburg
Salubindza
Mokopane
Mpumalanga
Sikhalasenkosi
Worcester
Mankweng
Stellenbosch
Naas
Uitkomsdal
Kroonstad
Ermelo
South Africa (ZAF) = ± s min = City population, log s C i t y G D P , l o g y Johannesburg
Cape Town
Durban
Pretoria
Klipgat
Port Elizabeth
Evaton
Tsakane
Edendale
Bloemfontein
East London
Rustenburg
Polokwane
Osizweni
Vanderbijlpark eGobhoza
Phuthaditjhaba
Paarl
Kimberley
Somerset West
Emalahleni
Middelburg
Botshabelo
Mafikeng
George
Bronville
KwaMhlanga
Potchefstroom
Jouberton
Vosman eMbalenhle
Sasolburg
Salubindza
Mokopane
Mpumalanga
Sikhalasenkosi
Worcester
Mankweng
Stellenbosch
Naas
Uitkomsdal
Kroonstad
Ermelo
South Africa (ZAF) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Zambia (ZMB) = ± s min = City population, log s C i t y r an k , l o g r Lusaka
Kitwe
Ndola
Mansa
Kasama
Chingola
Kabwe
Chipata
Kapiri Mposhi
Livingstone
Choma
Mufulira
Tunduma
Mbala
Solwezi
Mongu
Nchelenge
Monze
Lundazi
Kafue
Luanshya
Kalomo
Mpulungu
Mumbwa
Mwinilunga
Samfya
UNNAMED
Mazabuka
Isoka
Chinsali
Mkushi
Chililabombwe
Zambia (ZMB) = ± s min = City population, log s C i t y G D P , l o g y Lusaka
Kitwe
Ndola
Mansa
Kasama
Chingola
Kabwe
Chipata
Kapiri Mposhi
Livingstone
Choma
Mufulira
Tunduma
Mbala
Solwezi
Mongu
Nchelenge
Monze
Lundazi
Kafue
Luanshya
Kalomo
Mpulungu
Mumbwa
Mwinilunga
Samfya
UNNAMED
Mazabuka
Isoka
Chinsali
Mkushi
Chililabombwe
Zambia (ZMB) = ± City population, log s C o m p l e m en t a r y c u m u l a t i v e d i s t r i bu t i on , l o g F ( s ) Zimbabwe (ZWE) = ± s min = City population, log s C i t y r an k , l o g r Harare
Bulawayo
Gweru
Kwekwe
Mutare
Glenclova
Bindura
Masvingo
King Mine
Kadoma
Norton
Chinhoyi
Triangle
Chegutu
Marondera
Zimbabwe (ZWE) = ± s min = City population, log s C i t y G D P , l o g y Harare
Bulawayo
Gweru
Kwekwe
Mutare
Glenclova
Bindura
Masvingo
King Mine
Kadoma
Norton
Chinhoyi
Triangle
Chegutu
Marondera
Zimbabwe (ZWE) = ±0.07