World influence and interactions of universities from Wikipedia networks
EEPJ manuscript No. (will be inserted by the editor)
World influence and interactions of universities from Wikipedianetworks
C´elestin Coquid´e , Jos´e Lages , and Dima L. Shepelyansky Institut UTINAM, Observatoire des Sciences de l’Univers THETA, CNRS, Universit´e de Bourgogne Franche-Comt´e, Besan¸con,France Laboratoire de Physique Th´eorique, IRSAMC, Universit´e de Toulouse, CNRS, UPS, 31062 Toulouse, FranceReceived: / Revised version: date
Abstract.
We present Wikipedia Ranking of World Universities (WRWU) based on analysis of networksof 24 Wikipedia editions collected in May 2017. With PageRank and CheiRank algorithms we determineranking of universities averaged over cultural views of these editions. The comparison with the Shanghairanking gives overlap of 60% for top 100 universities showing that WRWU gives more significance totheir historical development. We show that the new reduced Google matrix algorithm allows to determineinteractions between leading universities on a scale of ten centuries. This approach also determines theinfluence of specific universities on world countries. We also compare different cultural views of Wikipediaeditions on significance and influence of universities.
PACS.
The importance of universities for progress of humanityis broadly recognized world wide. Thus in 2017 UNESCOemphasizes the role of universities and higher educationinstitutes in fostering sustainable development and em-powering learners [1]. The efficiency of university educa-tion gained a high political importance in many worldcountries. Various tools have been developed to measurequantitatively this efficiency among which the rankingof universities gained significant importance as reviewedin [2]. Thus the Academic Ranking of World Universi-ties (ARWU), compiled by Shanghai Jiao Tong Univer-sity since 2003 (Shanghai ranking) [3], generated a signif-icant political impact on evaluation of higher educationefficiency in many countries [2]. For example, the ARWUstimulated the emergence of LABEX, IDEX projects inFrance [4] and the Russian Academic Excellence Project[5] with allocation of significant financial supports. In ad-dition to ARWU other international ranking systems ofuniversities appeared (see e.g. [6,7,8]). Various strong andweak features of ranking methodology are reviewed in [9,10,11]. Of course, the ranking systems are based on differ-ent specific criteria with different cultural preferences ofrather larger groups realizing these rankings. Already, thepresence of many ranking systems indicates the presenceof bias in each of above ranking systems. a email address: [email protected] b email address: [email protected] c email address: [email protected] Another purely mathematical and statistical approachto ranking of world universities has been developed in [12,13,14] on the basis of Google matrix analysis of Wikipedianetworks. For each Wikipedia language edition a networkis composed by all Wikipedia articles with directed linksbetween them generated by mutual quotations of a givenarticle to other articles. In [12] the analysis was performedonly for English Wikipedia (ENWIKI) of year 2009, otheryears for ENWIKI were considered in [13], while in [14]this analysis was done with 24 language Wikipedia edi-tions of 2013 that allowed to reduce significantly culturalbias (these 24 networks had been collected and analyzedfor historical figures in [15] in the frame of EC FET Openproject NADINE [16]). The Google matrix analysis [12,13,14] is based on the PageRank algorithm [17] which de-tailed description is given in [18]. Some additional char-acteristics have been also used for description of networknodes (Wikipedia articles), like CheiRank and 2DRank,as described in [19,20]. Thus the Wikipedia Ranking ofWorld Universities (WRWU2013) from 24 Wikipedia net-works was introduced in [14] and it was shown that itstop 100 universities has 62% overlap with ARWU. In ad-dition WRWU2013 attracted a significant interest worldwide (see [21] and various press highlights listed at [22]).Other research groups also start to apply Wikipedia rank-ing in Wikiometrics [23]. We also note the growing interestto scientific analysis of several language editions of Wiki-pedia [24].In this work we extend the WRWU studies startedin [14]. The new elements are: we use 24 Wikipedia edi- a r X i v : . [ c s . S I] S e p C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks tions collected in May 2017 [25] and also we apply therecently invented reduced Google matrix (REGOMAX)method [26]. This new method allows to determine effec-tive interactions between a selected relatively small subsetof network nodes taking into account all pathways be-tween them via the global huge network with millionsof nodes. The efficiency of the REGOMAX method hasbeen demonstrated on examples of analysis of interactionsof political leaders [27], terror networks [28] and protein-protein interactions in cancer networks [29]. Here, usingthe REGOMAX method we obtain effective interactionsbetween a group of selected universities and determinetheir influence on world countries. The new ranking of uni-versities from Wikipedia 2017 editions is compared withthose of 2013.The paper is composed as follows: Section 2 gives de-scription of network datasets; Section 3 describes Googlematrix construction and PageRank, CheiRank algorithmswith overview of the reduced Google matrix approach;Section 4 presents results on global ranking of universitiesfrom 24 editions and their distribution over world coun-tries; Section 5 provides REGOMAX results for Englishedition determining the world influence of specific uni-versities; the interactions between top 20 universities areanalyzed in Section 6 comparing views of English, French,German and Russian editions; in Section 7 we obtainedthe reduced Google matrix of top 100 universities aver-aged over 24 editions and analyze the interactions betweenuniversities on the scale of 10 centuries and all continents;discussion of the results is given in Section 8. All detailedranking results of WRWU2017 are available at [30] andcomplementary figures and tables are in SupplementaryInformation (see from p. 18).
We use the datasets of 24 Wikipedia editions extracted inMay 2017 [25] (see also [30]). The size of each network isgiven in Table 1. Compared to 2013 discussed in [15] thereis a significant size increase for each edition, especially forSwedish (SV) where a part of articles is now computergenerated. The number of links is given at [30]. On averagethere are about 20 links per node. Self-citation links arenot considered (references on the article inside the samearticle are eliminated).
The mathematical grounds of this study are based onMarkov chain theory and, in particular, on the Googlematrix analysis initially introduced in 1998 by Google’sco-founders, Brin and Page [17], for hypertext analysisof the World Wide Web. Let us consider the network ofthe N articles of a given Wikipedia edition. The network adjacency matrix element A ij is equal to 1 if article j quotes article i and equal to 0 otherwise. The Googlematrix element G ij = αS ij + (1 − α ) /N gives a transi-tion probability that a random reader jumps from arti-cle j to article i . The stochastic matrix element S ij is S ij = A ij / (cid:80) Ni =1 A ij if article j quotes at least one otherarticle, otherwise S ij = 1 /N . The second term in G pro-portional to (1 − α ), where 0 . < α < α = 0 .
85 typical for WWW studies [18]. TheGoogle matrix G , constructed as described above, belongsto the class of Perron-Frobenius operators [18]. The eigen-vector P with the largest eigenvalue λ = 1 is the solutionof equation G P = P . This PageRank vector P has positiveor zero components and describes the steady-state prob-ability distribution of the Markov process encoded in theGoogle matrix G . Assuming an infinite random process,the vector component P i is proportional to the number oftimes a random reader reaches an article i . It is convenientto sort the vector components P , . . . , P N in descendingorder: the article associated to the highest (lowest) vectorcomponent has the top (last) rank index K = 1 ( K = N ).The PageRank algorithm measures the relative influenceof articles. Recursively, more an article is quoted by influ-ent articles, more high is its probability.As proposed in [31] we also consider the same networkof articles but with inverted links, i.e., article j pointstoward article i if article j is quoted by article i . Thisinverted network is defined by the adjacency matrix el-ements, A ∗ ij = A ji , which can be used to build succes-sively the corresponding stochastic matrix elements, S ∗ ij ,and the corresponding Google matrix elements, G ∗ ij . TheCheiRank vector P ∗ is then defined such as G ∗ P ∗ = P ∗ and the CheiRank is constructed similarly to the Page-Rank [31,12,19]. The CheiRank algorithm measures therelative communicative ability of the articles. Recursively,the more an articles quotes very communicative articles,the more it is communicative.The properties of the Google matrix spectrum andeigenstates and their various applications are discussedin detail in [18,19,20]. Table 1.
Wikipedia directed networks of 2017 from 24 con-sidered language editions; here N is the number of articles.Wikipedia data were collected in May 2017. Edition Language N Edition Language N EN English 5416537 ZH Chinese 939625SV Swedish 3786455 FA Persian 539926DE German 2057898 AR Arabic 519714NL Dutch 1900222 HU Hungarian 409297FR French 1866546 KO Korean 380086RU Russian 1391225 TR Turkish 291873IT Italian 1353276 MS Malaysian 289234ES Spanish 1287834 DA Danish 225523PL Polish 1219733 HE Hebrew 205411VI Vietnamese 1155932 EL Greek 130429JP Japanese 1058950 HI Hindi 121503PT Portuguese 967162 TH Thai 116495 ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 3
The concept of reduced Google matrix (REGOMAX) wasintroduced in [26] and tested with Wikipedia networks in[27,28] and protein-protein networks [29]. The method isbased on the construction of a Google matrix for a rela-tively small subset of nodes embedded into a much largernetwork taking into account all indirect interactions be-tween subset nodes via the remaining huge part of thenetwork.Let us consider a small subset S r of n r (cid:28) N articles,and the complementary subset S s of the n s = N − n r (cid:39) N remaining articles. For convenience, the Google matrix canbe rewritten as G = (cid:18) G rr G rs G sr G ss (cid:19) (1)where the submatrix G rr , of size n r × n r , encodes the tran-sitions between articles of the subset S r , the submatrix G ss , of size n s × n s , encodes the transitions between arti-cles of the subset S s , the submatrix G rs , of size n r × n s ,encodes the transitions from articles of the subset S s to-ward articles of the subset S r , the submatrix G sr , of size n s × n r , encodes the transitions from articles of the subset S r toward articles of the subset S s . Since G P = P , thePageRank vector can be rewritten as P = (cid:18) P r P s (cid:19) (2)where the vector P r ( P s ) of size n r ( n s ) contains the Pa-geRank vector components associated to articles of the S r ( S s ) subset. The reduced Google matrix G R associated toarticles of the subset S r is the n r × n r matrix defined im-plicitly by the following relation G R P r = P r . After somealgebra, the reduced Google matrix can be written as [26,27,29] G R = G rr + G ind where G ind = G rs (1 s − G ss ) − G sr . (3)Here 1 s is the n s × n s identity matrix. The reduced Googlematrix G R is composed by the G R -submatrix G rr whichencodes the direct links (direct quotations) between the n r articles of the S r subset and by an additional scatteringterm G ind which quantifies the indirect links between arti-cles. If there is no direct link from article j ∈ S r to article i ∈ S r , i.e., A ij = 0, then the corresponding G rr elementwill be minimum ( G rr ij ∼ /N ∼ − for the May 2017English Wikipedia network). Conversely, the correspond-ing G ind element can be very high highlighting the factthat two articles can be strongly indirectly linked throughsuccessive direct links between articles of the S s subset (eg, j ∈ S r → k ∈ S s → k ∈ S s → · · · → k n ∈ S s → i ∈ S r ).The PageRank vector of G R has the same components of n r nodes as in the global matrix G (up to a constant nor-malization factor). The reduced Google matrix G R , whichconserves the global Google matrix PageRank hierarchybetween the n r articles of the S r subset, encodes directlinks and effective indirect links between articles. The di-rect calculation of G ind converges very slowly since thematrix (1 s − G ss ) − is almost singular, indeed as n r (cid:28) n s , G ss ∼ G , the leading eigenvalue of G ss is λ c ∼
1. Letus associate to the eigenvalue λ c the right eigenvector Ψ R and the left eigenvector Ψ L such as G ss Ψ R = λ c Ψ R and Ψ TL Ψ R = 1. To speed up calculations, we followthe same procedure as in [26,27,29], splitting the term(1 s − G ss ) − in a term Ψ R Ψ TL (1 − λ c ) − which is a pro-jection onto the subspace associated to λ c and a term(1 s − Ψ R Ψ TL ) (1 s − G ss ) − which is a projection onto thecomplementary subspace. This procedure enables us torewrite the reduced Google matrix as G R = G rr + G pr + G qr (4)where G pr = G rs Ψ R Ψ TL G sr (1 − λ c ) − encodes essentiallyalready known information concerning the PageRank (since Ψ R ∼ P ) and G qr = G rs (1 s − Ψ R Ψ TL ) (1 s − G ss ) − G sr en-codes hidden interactions between articles which appeardue to indirect links via the global network [26,27,29].In the following we perform analysis of the three compo-nents present in (4), we also consider the matrix compo-nent G qrnd obtained from G qr by taking out the diagonalterms since the self-citations are not very interesting. Once the articles of 24 considered editions are ranked us-ing PageRank and CheiRank algorithms, we extract foreach edition the top 100 articles devoted to institutions ofhigher education and research. We also consider 2DRankwhich is a combination of PageRank and CheiRank (see[12,14]; 2DRank results are available at [30]). As in [15,14], from these 24 top 100 listings we obtain the followingcumulative score for a given university UΘ U,A = (cid:88) E (101 − R U,E,A ) (5)where A denotes the algorithm used for the ranking (Page-Rank or CheiRank or 2DRank), E the Wikipedia edition, R U,E,A the rank of university U in the top 100 universitiesobtained using algorithm A from edition E of Wikipedia.If an university U (cid:48) is absent from the top 100 universitiesobtained from an edition E (cid:48) with an algorithm A (cid:48) then weartificially set R U (cid:48) ,E (cid:48) ,A (cid:48) = 101. We use ISO 3166-1 alpha-2country codes [32] (all the used country codes are availableat [30]).The top 10 universities from WRWU2017 with Page-Rank algorithm and from ARWU2017 are given in Tab. 2and Tab. 3 respectively. The top 3 places of WRWU areoccupied by Oxford, Cambridge and Harvard while forARWU it is Harvard, Stanford and Cambridge. The uni-versities with significantly lower positions in WRWU (com-pared to ARWU) are MIT, Berkeley and Caltech, whileOxford significantly improves its position at WRWU goingto the first place from 7th at ARWU.The overlap between different rankings are presentedin Fig. 1. For the top 100 universities we have 60% overlap C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks j η ( j ) Fig. 1.
Left panel: Overlap η ( j ) = j c /j of ARWU2017 withWRWU2017 as a function of the rank j of WRWU2017. Here j c gives the number of common universities among the first j uni-versities of the two rankings. The color curves show the overlapof ARWU2017 with WRWU2017 (black curve), of ARWU2013with WRWU2013 (red curve), of ARWU2013 with ARWU2017(green curve), and of WRWU2013 with WRWU2017 (bluecurve). Right panel: Overlap of ARWU2017 with EN-WRWU2017 (black curve), of ARWU2017 with FRWRWU2017(red curve) and of ARWU2017 with DEWRWU2017 (bluecurve). The horizontal axis label j is the rank of ARWU2017. between WRWU PageRank list and ARWU list in 2017.For 2013 this overlap was slightly higher at 62%. The over-lap between WRWU2017 list and WRWU2013 list is 91%and between ARWU2017 list and ARWU2013 list is 84%.WRWU appears to be stable, top10s in 2013 (Tab. 2) and2017 (Tab. 3 in [14]) contain the same universities butwith some changes in places: Oxbridge keep the two firstplaces but Oxford supersedes Cambridge at the first place;Yale (9 →
5) and Chicago (7 →
6) improve their rankingwhereas Princeton (5 →
7) and MIT (6 →
9) recede; Har-vard (3 → → → →
10) keep their positions. Between 2013 [22] and2017 [30], only 9 universities went out from top100 (IPSA /Karolinska Institutet / Rockefeller / Rutgers / Tsinghua/ Amsterdam / Hamburg / Strasbourg / Wroc(cid:32)law) and9 new universities enter in the top100 (Seoul NationalUniversity / TU Munich / UC, San Diego / Boulder /Freiburg / Kiel / Marburg / Salamanca / Sydney).The above numbers and comparisons show that WRWUapproach gives a reliable ranking which remains relatively
Table 2.
List of the first 10 universities of the 2017 WikipediaRanking of World Universities using PageRank algorithm. Fora given university, the score Θ PR is defined by (5), N a is thenumber of appearances in the top 100 lists of 24 Wikipediaeditions, CC is the country code, LC is the language code, andFC is the foundation century. Rank Θ PR N a University CC LC FC1st 2281 24 University of Oxford UK EN 112nd 2278 24 University of Cambridge UK EN 133rd 2277 24 Harvard University US EN 174th 2099 24 Columbia University US EN 185th 1959 23 Yale University US EN 186th 1917 24 University of Chicago US EN 197th 1858 23 Princeton University US EN 188th 1825 21 Stanford University US EN 199th 1804 21 Massachusetts Institute of Technology US EN 1910th 1693 20 University of California, Berkeley US EN 19 close to ARWU at different years. At the same time WRWUhas about 40% of different universities compared to ARWU.The origin of this difference is based on variety of culturalviews well present in 24 editions. Thus the right panelof Fig. 1 shows a spectacular difference between EN, FRand DE editions: for top 10 universities the German edi-tion has only about 10% overlap with ARWU while ENand FR have about 50%. For top 100 this difference stillremains significant being approximately 34% for DE, 43%for FR and 60% for EN. Thus the case of German editiondemonstrates rather different cultural view on importanceof their universities. As discussed in [14] there are clearhistorical grounds for this difference related to the worlddominance of German and Italian universities before 19thcentury as it is clearly seen in Fig. 10 in [14].In total for all 24 editions we find 1011 and 1464 dif-ferent universities with PageRank and CheiRank algo-rithms respectively. Their geographical distribution overthe country world map is shown in Fig. 2. The largestnumber of top universities is in US but we see a signifi-cant numbers also for India, Japan, Germany and Francefor PageRank which characterizes the university influence.The communicativity is highlighted by CheiRank with topcountries being US, India, Japan, France and China. Ofcourse, Hindi, Japan, Chinese editions give certain prefer-ence to their own universities but in global the high posi-tions of these universities and countries reflect significantefforts in higher education performed by these countries.The geographical distributions of top 100 universitiesof ARWU2017 and WRWU2017 are presented in Fig. 3.For ARWU the top countries are US, UK, Australia andChina while for WRWU we find US, Germany, UK andJapan. It is clear that ARWU gives too high significance toAnglo-saxon and Chinese universities while WRWU pro-vides more balanced historical view taking into account asignificant role played e.g. by German universities.A more detailed view on the universities distributionover countries for ARWU and WRWU is shown in Fig. 4.The ranking of WRWU universities inside each country isgiven in [30].
Table 3.
List of the first 10 universities of ARWU2017 [3].The last columns show the difference between ARWU2017 rankand WRWU2017 rank.
Rank ARWU17 WRWU171st Harvard University -22nd Stanford University -63rd University of Cambridge +14th Massachusetts Institute of Technology -55th University of California, Berkeley -56th Princeton University -17th University of Oxford +68th Columbia University +49th California Institute of Technology -1310th University of Chicago +4 ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 5
Fig. 2.
Geographical distribution of the universities enteringthe 2017 Wikipedia Ranking of World Universities using Pa-geRank (top panel) and CheiRank algorithms (bottom panel).The total number of universities is 1011 (1464) for WRWU us-ing PageRank (CheiRank) algorithm. US universities are themost numerous: 101 (174) universities for WRWU using Page-Rank (CheiRank) algorithm. Countries with white color haveno universities in the top 100 edition lists. Here and below thecolor categories are obtained using the Jenks natural breaksclassification method [33].
In this Section we use the REGOMAX approach to ana-lyze the influence of universities on world countries. Withthis aim the reduced Google matrix is constructed for thesubset of articles devoted to the PageRank top 20 univer-sities of ENWRWU (see Tab. 4) and articles devoted tothe 85 countries to which belong universities appearing inWRWU (see Tab. 5). Thus the total size of the reducedGoogle matrix is n r = 105, to be compared to the globalENWIKI network size which is about 5.4 millions articles. Table 4.
List of the PageRank top 20 universities of Englishedition WRWU2017. The color code corresponds to the re-gional location of universities: red for US west coast, orangefor US central region, blue for US east coast, and violet forUK.
Rank University Rank University1st
Harvard University
University of Michigan
University of Oxford
Cornell University
University of Cambridge
University of California, Los Angeles
Columbia University
University of Pennsylvania
Yale University
New York University
Stanford University
University of Texas at Austin
Massachusetts Institute of Technology
University of Florida
University of California, Berkeley
University of Edinburgh
Princeton University
University of Wisconsin-Madison
University of Chicago
University of Southern California
Fig. 3.
Geographical distribution of the first 100 universitiesfrom ARWU2017 (top panel) and WRWU2017 from PageRank(bottom panel). US universities are the most numerous, 48 uni-versities for ARWU2017 and 37 universities for WRWU2017. U S U K A
U CH C A D E N L F R J P SE BE
CN D K F I I L N O RU S G Foundation country o f un i v e r s i t i e s (a) U S D E U K J P CH I T SE C A F R N L P L RU A T A U CN C Z D K EE E G ES F I I E I L K R M X N O P T Foundation country o f un i v e r s i t i e s (b) U S I N J P D E F R K R T R T H CN U K I T M Y P L RU B R ES HU G R I R SE I D N L V N D
K E G Foundation country % o f un i v e r s i t i e s (c) Fig. 4.
Distribution over countries of (a) 2017 ARWU top 100universities and of (b) 2017 WRWU top 100 universities. Panel(c) gives the percentage per country of universities among the1011 universities listed in 2017 WRWU, countries with lessthan 10% are not shown. Countries with equal number of uni-versities are sorted by alphabetic order.
The images of the corresponding reduced Google ma-trix G R and its components G rr , G pr , and G qr , are shownin Fig. 5. As discussed above and in [27] the G pr compo-nent is rather close to the matrix composed by identicalcolumns of PageRank vector of n r nodes, the direct linksare presented by the component G rr and indirect linksby G qr (and related G qrnd ). The weights of these threecomponents (sum of elements of all columns divided by C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks matrix size n r ) are respectively W R = 1, W pr = 0 . W rr = 0 . W qr = 0 . G rr and G qr are small, compared to thoseof G pr , but these two components provide new importantinformation on interactions between nodes. The weight ofindirect links is larger than the direct ones W qr > W rr .The knowledge of all matrix elements of G R allows usto determine the influence or sensitivity of a given univer-sity u on a given country c . To measure the sensitivity wechange the matrix element G R ( u → c ) by a factor (1 + δ )with δ (cid:28)
1, we renormalize to 1 the sum of the columnassociated to university u , and we compute the logarith-mic derivative of PageRank probability P ( c ) associatedto country c : D ( u → c, c ) = d ln P ( c ) /dδ (diagonal sen-sitivity). It is also possible to consider the nondiagonalsensitivity D ( u → c, c (cid:48) ) = d ln P ( c (cid:48) ) /dδ when the varia-tion is done for the link from u to c and the derivativeof PageRank probability is computed for another country c (cid:48) . This approach was already used in [28,34] showing itsefficiency. Table 5.
List of the countries associated to the universitiesappearing in WRWU2017. Countries are ranked from 2017 Wi-kipedia English edition using PageRank algorithm.
Rank University CC Rank University CC1 United States US 44 Chile CL2 France FR 45 Republic of Ireland IE3 Germany DE 46 Singapore SG4 United Kingdom UK 47 Serbia RS5 Iran IR 48 Vietnam VN6 India IN 49 Nepal NP7 Canada CA 50 Estonia EE8 Australia AU 51 Iraq IQ9 China CN 52 Bangladesh BD10 Italy IT 53 Syria SY11 Japan JP 54 Myanmar MM12 Russia RU 55 Slovakia SK13 Brazil BR 56 Venezuela VE14 Spain ES 57 Morocco MA15 Netherlands NL 58 Cuba CU16 Poland PL 59 Puerto Rico PR17 Sweden SE 60 Saudi Arabia SA18 Mexico MX 61 Lithuania LT19 Turkey TR 62 Lebanon LB20 Romania RO 63 Cyprus CY21 South Africa ZA 64 Latvia LV22 Norway NO 65 Belarus BY23 Switzerland CH 66 United Arab Emirates AE24 Philippines PH 67 Uruguay UY25 Austria AT 68 North Korea KP26 Belgium BE 69 Yemen YE27 Argentina AR 70 Costa Rica CR28 Indonesia ID 71 Tunisia TN29 Greece GR 72 Jordan JO30 Denmark DK 73 Guatemala GT31 South Korea KR 74 Greenland GL32 Israel IL 75 Dominican Republic DO33 Hungary HU 76 Uzbekistan UZ34 Finland FI 77 Kuwait KW35 Egypt EG 78 Qatar QA36 Portugal PT 79 Senegal SN37 Taiwan TW 80 El Salvador SV38 Ukraine UA 81 Suriname SR39 Czech Republic CZ 82 Faroe Islands FO40 Malaysia MY 83 Brunei BN41 Thailand TH 84 Palestine PS42 Colombia CO 85 Georgia GE43 Bulgaria BG
GEPSBNFOSRSVSNQAKWUZDOGLGTJOTNCRYEKPUYAEBYLVCYLBLTSAPRCUMAVESKMMSYBDIQEENPVNRSSGIECLBGCOTHMYCZUATWPTEGFIHUILKRDKGRIDARBEATPHCHNOZAROTRMXSEPLNLESBRRUJPITCNAUCAINIRUKDEFRUSUSCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a E d i n U W - M a d i s on U S CU S F RD E UK I R I NCAAUCN I T J P RUBR ES N L P L SE M X T RR O Z AN O CH P HA T B E AR I D G RDKKR I L HU F I E G P TT W UAC Z M Y T HC O B G C L I ES G R SV NN PEE I Q BD SY MM S K VE M ACU P R S A LTL BC Y L V B Y A E U Y K PYE CR T N J OG T G L D O U Z K W Q A S N SVS R F O BN PS G E GEPSBNFOSRSVSNQAKWUZDOGLGTJOTNCRYEKPUYAEBYLVCYLBLTSAPRCUMAVESKMMSYBDIQEENPVNRSSGIECLBGCOTHMYCZUATWPTEGFIHUILKRDKGRIDARBEATPHCHNOZAROTRMXSEPLNLESBRRUJPITCNAUCAINIRUKDEFRUSUSCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a E d i n U W - M a d i s on U S CU S F RD E UK I R I NCAAUCN I T J P RUBR ES N L P L SE M X T RR O Z AN O CH P HA T B E AR I D G RDKKR I L HU F I E G P TT W UAC Z M Y T HC O B G C L I ES G R SV NN PEE I Q BD SY MM S K VE M ACU P R S A LTL BC Y L V B Y A E U Y K PYE CR T N J OG T G L D O U Z K W Q A S N SVS R F O BN PS G E GEPSBNFOSRSVSNQAKWUZDOGLGTJOTNCRYEKPUYAEBYLVCYLBLTSAPRCUMAVESKMMSYBDIQEENPVNRSSGIECLBGCOTHMYCZUATWPTEGFIHUILKRDKGRIDARBEATPHCHNOZAROTRMXSEPLNLESBRRUJPITCNAUCAINIRUKDEFRUSUSCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a E d i n U W - M a d i s on U S CU S F RD E UK I R I NCAAUCN I T J P RUBR ES N L P L SE M X T RR O Z AN O CH P HA T B E AR I D G RDKKR I L HU F I E G P TT W UAC Z M Y T HC O B G C L I ES G R SV NN PEE I Q BD SY MM S K VE M ACU P R S A LTL BC Y L V B Y A E U Y K PYE CR T N J OG T G L D O U Z K W Q A S N SVS R F O BN PS G E GEPSBNFOSRSVSNQAKWUZDOGLGTJOTNCRYEKPUYAEBYLVCYLBLTSAPRCUMAVESKMMSYBDIQEENPVNRSSGIECLBGCOTHMYCZUATWPTEGFIHUILKRDKGRIDARBEATPHCHNOZAROTRMXSEPLNLESBRRUJPITCNAUCAINIRUKDEFRUSUSCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a E d i n U W - M a d i s on U S CU S F RD E UK I R I NCAAUCN I T J P RUBR ES N L P L SE M X T RR O Z AN O CH P HA T B E AR I D G RDKKR I L HU F I E G P TT W UAC Z M Y T HC O B G C L I ES G R SV NN PEE I Q BD SY MM S K VE M ACU P R S A LTL BC Y L V B Y A E U Y K PYE CR T N J OG T G L D O U Z K W Q A S N SVS R F O BN PS G E Fig. 5.
Reduced Google matrix G R for the first 20 universitiesranked in ENWRWU (Tab. 4) and the 85 countries to whichuniversities from WRWU belong (Tab. 5). The full reducedGoogle matrix G R is presented in top left panel, G pr in topright panel, G rr in bottom left panel, and G qrnd in bottomright panel. The weights of G R matrix components are W R = 1, W pr = 0 . W rr = 0 . W qr = 0 . The world maps of university influence on countries,expressed by the diagonal sensitivity D ( u → c, c ) for 4selected universities, are shown in Fig. 6.For Harvard the most sensitive country is South Africa(ZA) due to the well known scandal linked to Harvard in-vestments in apartheid ZA pointed on the Harvard wiki-page. Puerto Rico also appears on this wikipage in relationwith oldest universities in the America. However, next in-fluenced countries are Georgia (GE), Israel (IL) and Ire-land (IR) which are not present on the wikipage whichappearance we attribute to indirect links.For Chicago the most influenced countries are Singa-pore (SG), Puerto Rico (PR) and India (IN). The first twocountries SG, PR are not present on the wikipage showingthat indirect links play an important role for them. Indiahas a direct link related to the following facts: Chicagocampus opened in India and a faculty member was erst-while governor of India central bank.For Stanford the top countries are Spain (ES), presenton the wikipage, PR and ZA appearing due to indirectlinks.For Oxford the top three countries are Jordan (JO),appearing of wikipage since Abdullah II of JO has beeneducated at Oxford; Iraq (IQ), also appearing on wikipagesince T. E. Lawrence educated at Oxford played a majorrole in establishing and administering the modern stateof IQ; IR which is not present on wikipage but has closelinks with UK. ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 7 Fig. 6.
World map of diagonal sensitivity of world countries D ( u → c, c ) to the change of the reduced Google matrix linkuniversity u → country c . The cases of 4 universities are shownfrom top to bottom: Harvard University, University of Chicago,Stanford University, and University of Oxford. Examples of nondiagonal sensitivity are shown in Fig. 7for the link variation Harvard University to US and Uni-versity of Oxford to UK. For the link Harvard → US themost influenced countries are Suriname (SR), People’s Re-public of Korea (KP) and Puerto Rico (PR). For the linkvariation Oxford → UK the most influenced countries areQatar (QA), Ireland (IR) and Singapore (SG). By defi-nition the nondiagonal sensitivity contains indirect effectsand it is not so easy to find the pathways of links which are
Fig. 7.
World map of nondiagonal sensitivity D ( u → c, c (cid:48) ) ofcountry c (cid:48) to the change of the reduced Google matrix linkHarvard → US (top panel) and Oxford → UK (bottom panel).Red (blue) color corresponds to the greatest (lowest) absolutevalue. Diagonal values D ( u → c, c (cid:48) = c ) are not shown. responsible for this dominant influence. These examplesshow the strength of reduced Google matrix approach. Fig. 8.
Same as in Fig. 6 with diagonal sensitivity D (“Rice University” → c, c ) to the change of the reducedGoogle matrix link Rice University → country c . Finally we discuss an example of Rice University. It hasrank 74 in ARWU2017 being at position 37 inside USA,but according to WRWU2017 its PageRank position isonly 357 and 56 inside USA. This shows that the Wikipe-dia article of Rice University is not sufficiently developedand its visibility via Wikipedia is rather low and can beimproved by more skillful organization of its wikipage. Wenote that Wikipedia visibility of a university plays ratherimportant role since very often it is on top lines of Googlesearch and many language editions spread the wikipagecontent world wide free of charge. Also the WRWU po-sition 357 is only due to appearance of Rice in top 100
C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks
USCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L A U P e nn N Y U U T A u s t i n F l o r i d a E d i n U W - M a d i s on U S C USCUW-MadisonEdinFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaCambridgeOxfordHarvard H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L A U P e nn N Y U U T A u s t i n F l o r i d a E d i n U W - M a d i s on U S C Fig. 9.
Matrices G rr (left panel) and G qrnd (right panel) fortop20 ENWRWU (Tab. 4). The universities are ordered bytheir PageRank index as in Tab. 4. The matrix weights are W rr = 0 . W qrnd = 0 . universities of FA, KO, and TH language editions prob-ably due to wikipage creation and information given byRice alumni speaking these languages. This indicates animportance of links between university and its alumni.The world influence of Rice University, expressed viaits diagonal sensitivity, is shown in Fig. 8. The most in-fluenced countries are Kuwait (KW), Mexico (MX) andPuerto Rico (PR). These countries are not present on thewikipage of Rice University and their appearance is re-lated to indirect links. In this Section we analyze the interactions between top 20universities obtained from the REGOMAX approach. Weconsider the different cultural views from EN, FR, DE,RU editions and make a comparative analysis. For ENedition we also consider the links of selected universitieswith countries.
Top 20 PageRank universities of ENWRWU2017 are givenin Tab. 4. They are either US or UK universities. We define4 regional groups with their PageRank leaders: StanfordUniversity for US west coast, University of Chicago forUS central region, Harvard University for US east coast,and University of Oxford for UK; each group is markedby color in Tab. 4.The components of reduced Google matrix describingdirect links G rr and indirect links G qrnd are shown in Fig. 9(only nondiagonal links are shown for G qr ). The weight ofindirect nondiagonal links is about 50% percent strongerthan the weight of direct links. This shows the importanceof indirect interactions between top 20 universities.To characterize the importance of direct and indirectlinks we consider the sum of two matrix components givenby G rr + G qrnd . From this matrix we construct the net-work of friends of regional leaders shown in Fig. 10 (the Fig. 10.
Network of friends of top 20 PageRank universities ofENWRWU obtained from matrix of direct and indirect links G rr + G qrnd . Color filled nodes are regional leaders. Red linksare purely hidden links, i.e., no corresponding adjacency ma-trix entry. We obtain 4 friendship levels (gray circles). Linksoriginating from 1st level universities are presented by solidlines, from 2nd level by dashed lines, from 3rd level by dotedlines, and from 4th level by “ \ ” symbol lines. Fig. 11.
Network of friends from G rr + G qrnd associated to thetop20 ENWRWU and 85 countries listed in Tab. 5. For eachregional leaders, Stanford University, University of Chicago,Harvard University, University of Oxford, the four strongestlinks to one of the 85 countries listed in Tab. 5 are presented.Universities (countries) are represented by empty (full) nodes.The color code for countries depends on the main spoken lan-guage: blue for English, red for Arabic, orange for Spanish, violet for Chinese, green for Hindi, and yellow for Hebrew.Red links are purely indirect links and black ones are fromdirect links. drawings of networks have been produced using Cytoscape[35]). First we place the regional leader on a circle (1stlevel of possible friendship). From a regional leader welook at the four biggest outgoing links in G rr + G qrnd ,these four links define the four best friends of the regionalleader. If these friends are not present in the network of ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 9 friends, i.e., they are not themselves regional leaders, thenthey are placed on the circle around the regional leader(2nd level of friendship). If several regional leaders sharethe same friend, by preference, the friend is placed in thecircle around the leader of its region. Then, from eachfriends of regional leaders, we define in the same way fournew friends. Each new friend is either already placed in thefriendship network or not. If the new friend is not present,it is placed in the circle around the corresponding friend ofregional leader (3rd level of friendship). If a new friend isshared by several friends of regional leaders, the new friendis placed by preference on the circle around the friend ofregional leader belonging to its region. In the same mannerwe then define the 4th level of friendship and so on. Theprocedure continues until no new friends can be placedon the friendship network (because already placed on it).For the 2017 ENWRWU top20 the procedure stops afterfour levels of friendship. A red arrow represents a purehidden link, i.e., a link from university u to university u (cid:48) with a null adjacency matrix entry, A u (cid:48) u = 0, or otherwisestated, with a minimal value in G rr , ( G rr ) u (cid:48) u = (1 − α ) /N .This network presentation of friends in Fig. 10 showsthat the close friends are mainly located in same region;thus MIT, Harvard, Yale form one group of east coast, Ox-ford, Cambridge, Edinburgh are friends inside UK. How-ever, there are also inter-regional friends formed by Prince-ton, UCLA, USC, UT Austin and proximity between Stan-ford, Berkeley and Cornell. The direct links shown in blackplay an important role but indirect links shown in redare also present and significant like e.g. MIT being indi-rect friend of Stanford, Harvard being indirect friend ofChicago and Oxford, and Edinburgh, Princeton being in-direct friend of Oxford.We also consider countries which are friends of eachregional university leader as shown in Fig. 11. For this weconsider the matrix elements of G rr + G qrnd constructedfor top 20 universities of Tab. 4 and 85 countries listed inTab. 5. For each regional leader university we select top4 friendliest countries. The network of country-universityfriends is presented in Fig. 11 with countries marked bycolors corresponding to mostly spoken language. Thus wesee that countries friends of Oxford are mostly Arab andEnglish speaking countries; countries friends of Harvardare dominantly from English speaking countries except-ing one Hebrew speaking country; friends of Stanford aretwo Spanish speaking countries, one English and one He- Table 6.
List of top 20 PageRank universities of French edi-tion WRWU2017. The color code corresponds to the countrylocation of universities: blue for US, violet for UK, red for FR,green for CA, and yellow for BE.
Rank University Rank University1st
Harvard University
University Laval
University of Oxford
Pantheon-Sorbonne University ´Ecole polytechnique
Princeton University
University of Cambridge
University of California, Berkeley ´Ecole normale sup´erieure
Paris-Sorbonne University
Massachusetts Institute of Technology
Universit´e libre de Bruxelles
Yale University
University of Montreal
Columbia University
Universit´e catholique de Louvain
Stanford University
Paris Nanterre University ´Ecole pratique des hautes ´etudes
University of Chicago
Fig. 12.
Same as in Fig. 10 for PageRank top 20 universities ofFRWIKI2017 from Tab. 6. Color filled nodes are country lead-ers. Red links are purely hidden links, i.e., no correspondingadjacency matrix entry. We obtain 4 friendship levels (gray cir-cles). Links originating from 1st level universities are presentedby solid lines, from 2nd level by dashed lines, from 3rd level bydoted lines, and from 4th level by “ \ ” symbol lines. brew; Chicago is mostly diversified having English, Hindi,Chinese and Spanish speaking friends. Here we consider the cultural view of FRWIKI on top20 universities and their interactions. We select from FR-WIKI2017 top PageRank universities listed in Tab. 6. Theseuniversities belong to 5 countries (US, UK, FR, CA, BE)marked by corresponding color. Top PageRank universityof each country is considered as a country leader. Similarto the case of Fig. 10 we obtain from the reduced Googlematrix components G rr + G qrnd of these 20 universities thenetwork of friends shown in Fig. 12.The obtained network of friends of Fig. 12 shows clearcluster of universities inside their own countries. How-ever, the inter-country links are well present and theyare mainly indirect links (shown in red) pointing towardEnglish speaking universities. Thus Princeton is indirectfriend of Oxford, ULaval and ULB; Yale and Harvardare indirect friends of ULaval. Since we consider FRWIKIthere are 6 French universities being the next in num-ber after US with 7 universities among top 20. However,US universities are strongly linked with universities ofCanada, Belgium and UK while French universities areweakly linked to other countries. This FRWIKI-analysisdemonstrate certain world isolation of French universi-ties. Also from FRWIKI point of view, the leading Englishspeaking universities in Fig. 12 form an invariant subsetfrom which a random surfer cannot escape: the friends ofthese universities are uniquely English speaking universi-ties. Fig. 13.
Same as in Fig. 10 for PageRank top 20 universities ofDEWIKI2017 from Tab. 7. Color filled nodes are country lead-ers. Red links are purely hidden links, i.e., no correspondingadjacency matrix entry. We obtain 4 friendship levels (gray cir-cles). Links originating from 1st level universities are presentedby solid lines, from 2nd level by dashed lines, from 3rd level bydoted lines, and from 4th level by “ \ ” symbol lines. Top 20 PageRank universities are given in Tab. 7. Thenetwork of friends, constructed for these 20 nodes fromthe matrix components G rr + G qrnd of the reduce Googlematrix, is shown in Fig. 13. A specific point of these top 20universities is that there are only 3 non-German-speakinguniversities (Harvard, Oxford, Cambridge). This is dueto the already discussed feature of DEWIKI which givesstrong preference to German universities (see right panelof Fig. 1). The universities belong only to 4 countries AT,DE, UK, US. The main cluster are formed around LMUMunich and Vienna however GU Frankfurt, Marburg andTubingen are closely linked with Oxford and Cambridge;Hamburg is linked with Harvard. It should be pointed thatthere is a dominance of indirect links which are also linkingdifferent countries. Table 7.
List of top 20 PageRank universities of German edi-tion WRWU2017. The color code corresponds to the countrylocation of universities: green for DE, blue for US, violet forUK, and black for AT.
Rank University Rank University1st
Ludwig Maximilian University of Munich
University of Freiburg
Humboldt University of Berlin
University of Cologne
University of G¨ottingen
University of M¨unster
Heidelberg University
University of Oxford
Free University of Berlin
University of Hamburg
University of Vienna
Goethe University Frankfurt
University of T¨ubingen
University of Cambridge
Harvard University
University of Marburg
University of Bonn
University of Kiel
Leipzig University
University of Jena
Fig. 14.
Same as in Fig. 10 for PageRank top 20 universitiesof RUWIKI2017 from Tab. 8. Color filled nodes are countryleaders. Reduced network from top20 RUWRWU G rr + G qrnd .Color filled nodes are regional leaders. Red links are purelyhidden links, i.e., no corresponding adjacency matrix entry. Weobtain 3 acquaintance levels (gray circles). Links originatingfrom 1st level universities are presented by solid lines, from2nd level by dashed lines, and from 3rd level by doted lines. Top 20 PageRank universities are given in Tab. 8. Thenetwork of friends, constructed for these 20 nodes fromthe matrix components G rr + G qrnd of the reduce Googlematrix, is shown in Fig. 14. Among these 20 universitiesthere 8 from US, 5 from Russia, 2 from Ukraine, 2 fromGermany (its former DDR part), 2 from UK and 1 fromAustria so that there are 6 different countries. The clustersof universities are mainly linked with their own countrieseven if there is very close proximity between UK and USeven if Berkeley and Chicago are in the circle proximity ofVienna. The main intercountry links are mainly indirect(except direct links between Kiev pointing to Moscow andSt. Petersburg which were all inside former USSR). It isinteresting to note that German university, belonging tothe former DDR part of Germany, have strong links withRussian universities, showing that the links inside Sovietblock are still significant even if Wikipedia had been cre-ated well after disappearance of DDR. Table 8.
List of top 20 PageRank universities of German edi-tion WRWU2017. The color code corresponds to the countrylocation of universities: red for RU, blue for US, violet for UK,green for DE, black for AT, and yellow for UA.
Rank University Rank University1st
Moscow State University
Kazan Federal University
Saint Petersburg State University
National University of Kharkiv
Harvard University
Stanford University
University of Oxford
Princeton University
University of Cambridge
University of Chicago
Massachusetts Institute of Technology
Higher School of Economics
Yale University
Bauman Moscow State Technical University
Columbia University
Leipzig University
Kyiv University
University of Vienna
Humboldt University of Berlin
University of California, Berkeley ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 11
NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v Fig. 15.
Reduced Google matrix G R for universities listedin Tab. 9 computed from EN (top left), FR (top right), DE(bottom left), and RU (bottom right) Wikipedia editions; foreach edition nodes have the same order as in Tab. 9. The imagesof components G pr , G rr , G qrnd are given in Figs. SI6, SI7, SI8. In this subsection we perform a comparison of differentcultural views of DEWIKI, ENWIKI, FRWIKI and RU-WIKI on top universities. With this aim we take 20 PageR-anked universities of each of these editions. This gives us52 different universities presented in these editions. Thelist of them is given in Tab. 9. Each of these universities isattributed to its own foundation country shown by colorsin this Table. There are 9 different countries: US, FR, DE,UK, CA, RU, AT, BE and UA.Then we perform the reduced Google matrix analysisfor these 52 universities for each edition constructing G R and its 3 components. The matrices G R for each editionare shown in Fig. 15. The G pr , G rr , G qrnd matrix compo-nents are available in Figs. SI6, SI7, SI8 with their weightswhich are similar to those given in Fig. 5; the weights ofdirect and indirect links are comparable. From Fig. 15 wesee that each edition has its own view on these 52 uni-versities. Indeed, there is a clear tendency that editionrank higher universities belonging to the countries withedition language, e.g. RUWIKI places Moscow and St.Petersburg universities on top PageRank positions witha similar situation for DEWIKI. Using the matrix com-ponents of G rr + G qrnd we analyze the network of friendof 52 universities from the view point of ENWIKI, FR-WIKI, DEWIKI and RUWIKI. The approach is the sameas those used in network of friends discussed in the previ-ous subsection.The network of top friends for 52 universities in EN-WIKI is shown in Fig. 16. We see that the majority of links Fig. 16.
Network of friends of 52 universities listed in Tab. 9computed from G rr + G qrnd of ENWIKI. Color filled nodes arecountry leaders (same colors as in the Tab. 9). Red links arepurely hidden links, i.e., no corresponding adjacency matrixentry. We obtain 4 acquaintance levels (gray circles). Linksoriginating from 1st level universities are presented by solidlines, from 2nd level by dashed lines, from 3rd level by dotedlines, and from 4th level by “ \ ” symbol lines. are indirect (red) comparing to the direct links (black). Asexpected two clusters of English speaking universities arewell visible; in fact as in Fig. 12, these English speakinguniversities form an invariant subspace from which a ran-dom surfer cannot escape. These universities act as anattractor subset in this friendship network. Chicago is lo-cated aside as it was already visible in previous subsection Table 9.
List of the 52 different universities appearing in thetop20s of the EN, FR, DE, RU WRWU. Color code correspondsto country: US , FR , DE , UK , CA , RU , AT , BE and UA .Universities are ordered by countries (country groups are or-dered according to PageRanking of 2017 English Wikipedia).Within country groups universities are ordered according toPageRanking of 2017 English Wikipedia. Rank University Rank University1
Harvard University Heidelberg University Columbia University Free University of Berlin Yale University University of T¨ubingen Stanford University University of Bonn Massachusetts Institute of Technology University of Freiburg University of California, Berkeley University of Cologne Princeton University University of M¨unster University of Chicago University of Hamburg University of Michigan Goethe University Frankfurt Cornell University University of Marburg University of California, Los Angeles University of Kiel University of Pennsylvania University of Jena New York University University of Oxford University of Texas at Austin University of Cambridge University of Florida University of Edinburgh University of Wisconsin–Madison University Laval University of Southern California University of Montreal ´Ecole polytechnique Moscow State University ´Ecole normale sup´erieure Saint Petersburg State University ´Ecole pratique des hautes ´etudes Kazan Federal University Panth´eon-Sorbonne University Bauman Moscow State Technical University Paris-Sorbonne University University of Vienna Paris Nanterre University Universit´e Libre de Bruxelles Humboldt University of Berlin Kyiv University Leipzig University National University of Kharkiv Ludwig Maximilian University of Munich University of G¨ottingen
Fig. 17.
Same as in Fig. 16 but from FRWIKI. (see Fig. 10). A compact cluster of German universitiesis also well visible. We point that there are only 2 iso-lated French universities among top friends appearing inFig. 16; no university from other countries points towardthese 2 universities, and these 2 universities point exclu-sively toward UK/US universities. In total this networkof top friends has 13 US universities, 6 of DE, 3 of UK,3 of RU, 2 of UA, 2 of CA, 2 of FR. Since the networkis obtained from ENWIKI it is understandable that USuniversities (with UK ones) form the majority. However,German universities show their strength and significantinfluence. Comparing to them French university group issmall and not significant being placed behind Russian uni-versities. This network clearly shows the weak represen-tation and influence of French universities that reflects acertain reality.The network of top friends from FRWIKI is shown inFig. 17. Here we have the dominance of 13 German uni-versities, followed by 11 of US, 6 of France and 4 of Russia.Still the indirect links play a dominant or comparable rolewith the direct links. In this network the cluster structureis less visible, however as in Figs. 12 and 16 the clusterof US-UK universities is central and acts as an attractorsubset.Fig. 18 shows the network of top friends from DEWIKI.Here, naturally, the dominance of 14 German universitiesremains, to be compared with 11 of US, 3 of France, 3of UK and 2 of Russia. In global DE universities are dis-tributed over 3 clusters, and US over 2 clusters.The network of top friends from RUWIKI is shownin Fig. 19. The dominance of German universities is wellpresent here with 16 of them followed by 10 of US, 4 ofRussia and 3 of UK. Three major hubs are clearly visiblea German one centered around HU Berlin / Heidelberg /G¨ottingen, an US-UK one centered around Harvard andOxford, and a Russian one centered around Moscow SU.
Fig. 18.
Same as in Fig. 16 but from DEWIKI.
Fig. 19.
Same as in Fig. 16 but from RUWIKI.
The analysis of this subsection allows to establish mostclose links between top world universities. It also showsthe dominance of US and German universities.
Above we have considered ranking and interactions froma view point of a given edition. Using the reduced Google ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 13 matrix approach it is possible to perform an averaging overall 24 editions thus determining the averaged cultural viewon selected universities. With this aim, for each of the 24Wikipedia editions listed in Tab. 1, we select the subset ofarticles devoted to the 100 first PageRank universities ofWRWU (see Tab. SI1). Then we compute the correspond-ing reduced Google matrix ¯ G R averaged over 24 Wikipediaeditions. The averaging is defined by the relation¯ G R = 124 (cid:88) E G ( E )R (6)where G ( E )R is the reduced Google matrix (4) of the Wiki-pedia edition E . Each one of the 24 reduced Google ma-trices is written in the same basis corresponding to theordered PageRank list of 100 universities. For a given edi-tion E , reduced Google matrix entries corresponding to alink pointing toward an absent university in edition E areset to 0 and reduced Google matrix columns correspond-ing to absent universities in edition E are filled with 1 / G ( E )pr matrix components of the full reducedGoogle matrices G ( E )R .We note that the averaging of 24 G ( E )R matrices withequal weights gives us again the reduced Google matrixwhich performs an averaging over different cultural viewsof 24 editions.The PageRank vector computed from the averagedreduced Google matrix ¯ G R is presented in Tab. 10. Wesee that the rank order is changed comparing to the Θ -averaging (5) with the top 10 PageRank universities givenin Tab. 2 (list of top 100 is given in Tab. SI1). We see thatHarvard takes the first position instead of the third onein Tab. 2 and then Oxford and Cambridge are moved tosecond and third positions in Tab. 10. The top ten uni-versities of Tab. 10 have overlap of 100% with PageRankWRWU of Tab. 2 and 90% with ARWU of Tab. 3. It canbe discussed what ranking averaging over 24 cultural viewof editions is more appropriate: with Θ -averaging or withaveraging of G ( E )R . We think that both approaches are use-ful: in Θ -averaging all PageRanking vectors are completelyindependent while averaging of G ( E )R introduces some ad-ditional links which are not present in certain networkeditions.The obtained averaged Reduced Google matrix ¯ G R and its three components are shown in Fig. 20. In globalthe matrix structure is similar to those of individual edi-tions discussed above. The component ¯ G pr has the dom-inant weight but it is rather close to the columns of Pa-geRank vector and hence the interesting links are deter-mined by the components ¯ G rr and ¯ G qr which have compa-rable weights. It is well seen that there are indirect linkswhich are not present between direct ones.From the matrix of direct and indirect links ¯ G rr +¯ G qrnd we construct the interaction friendship network be-tween above considered 100 universities divided by certaingroups. Such a network takes into account cultural viewsof all 24 editions. We now show all links by the same black color since after averaging over 24 editions there is a sig-nificant mixture of direct and indirect links.In our first division, we mark universities by founda-tion time (century) periods: red for foundation years from1000 to 1300 AD, blue from 1300 to 1600 AD, green from1600 to 1800 AD and black from 1800 to 2000 AD. Eachtime period has its leader taken as a university with high-est rank position in this period. The resulting networkof friends in shown in Fig. 21. This network shows aninteresting evolution of interactions between universitiesthrough 10 centuries: the cluster of universities foundedin 11th-13h centuries, marked in red, is formed mainly byUK and Italian universities (one from Spain, group leaderis Oxford). This cluster transfers its influence via inter-action and links to next 14th-16th centuries universities,marked in blue, which are mainly from northern coun-tries including Scotland, Denmark, Germany, Sweden andNetherlands (group leader is Copenhagen). The influenceof these universities is transfered to 17th-18th centuriesuniversities, marked in green, being mainly near the bluecluster and located in the same countries with addition ofMoscow in Russia, Tartu in Estonia, Helsinki in Finland; Table 10.
Top100 2017 WRWU ordered according to averagedreduced Google matrix.
Rank PageRankvalue University Rank PageRankvalue University1 0.0633191 Harvard University 51 0.00659655 Univ. of Colorado Boulder2 0.0528587 Univ. of Oxford 52 0.00657266 Univ. of Glasgow3 0.0518905 Univ. of Cambridge 53 0.00636839 Univ. of Toronto4 0.0339304 MIT a
54 0.0063255 Stockholm University5 0.0301911 Columbia University 55 0.00624184 Univ. of T¨ubingen6 0.0283041 Yale University 56 0.00609986 Univ. of Texas at Austin7 0.0261455 Stanford University 57 0.00593539 Univ. of Virginia8 0.024318 UC Berkeley b
58 0.00584412 Imperial College London9 0.0229394 Princeton University 59 0.00582829 Carnegie Mellon University10 0.0215136 Univ. of Chicago 60 0.00579437 Univ. of Bonn11 0.0197203 Univ. of Copenhagen 61 0.00570673 Univ. of Minnesota12 0.0168679 HU Berlin c
62 0.00567465 Keio University13 0.0160439 Uppsala university 63 0.00557384 Univ. of Helsinki14 0.0148231 Univ. of Tokyo 64 0.00548871 King’s College London15 0.0135633 Moscow State University 65 0.0054485 Univ. of Florida16 0.0127305 Cornell University 66 0.00538279 Univ. of Zurich17 0.0126064 HUJI d
67 0.00536546 Univ. of Manchester18 0.0125732 Univ. of Pennsylvania 68 0.00523928 McGill University19 0.0120329 UCLA e
69 0.00507791 Free University of Berlin20 0.011732 Leiden University 70 0.00505635 Univ. of Washington21 0.011246 Caltech f
71 0.00505447 Univ. of Illinois U.-C.22 0.0112404 New York University 72 0.00497258 Brown University23 0.0112273 Univ. of Vienna 73 0.00491403 Univ. of Wisconsin-Madison24 0.0104997 Univ. of Edinburgh 74 0.00485964 Northwestern University25 0.0103698 Jagiellonian University 75 0.00480294 Univ. of Coimbra26 0.0101557 Univ. of Bologna 76 0.00479832 Univ. of Oslo27 0.0100089 Univ. of G¨ottingen 77 0.00477973 Univ. of Padua28 0.00987766 Heidelberg University 78 0.00476805 Georgetown University29 0.00982921 Univ. of Michigan 79 0.00475634 UNAM l
30 0.00974263 Lund University 80 0.00468635 Boston University31 0.00929623 LSE g
81 0.0045985 Ohio State University32 0.00918967 Johns Hopkins University 82 0.00458516 Michigan State University33 0.00909002 Univ. of Warsaw 83 0.00452351 Univ. of Geneva34 0.00902656 Seoul National University 84 0.00451385 Univ. of Marburg35 0.00877768 Leipzig University 85 0.00433353 Univ. of Salamanca36 0.00832413 Univ. of Munich h
86 0.0042273 Univ. of Freiburg37 0.00791791 Waseda University 87 0.00418341 Univ. of Arizona38 0.0076835 Univ. College London 88 0.00417181 Univ. of Jena39 0.00751886 Duke University 89 0.00415139 MLU m
40 0.00718132 Sapienza i
90 0.00401368 Univ. of St Andrews41 0.00711981 ETH Zurich 91 0.00398415 TU Berlin n
42 0.0071081 USC j
92 0.00391916 UNC Chapel Hill o
43 0.00693105 ´Ecole Polytechnique 93 0.00390789 Univ. of Tartu44 0.00692597 Peking University 94 0.00388656 TU Munich p
45 0.00682986 Al-Azhar University 95 0.00385376 Univ. of Sydney46 0.00682254 ´Ecole Normale Sup´erieure 96 0.00384341 UC San Diego q
47 0.00680075 Kyoto University 97 0.00371085 Trinity College, Dublin48 0.00666809 Charles University 98 0.00368454 Indiana University49 0.00666454 SPbU k
99 0.00355122 University of Notre Dame50 0.00662585 Utrecht University 100 0.00353878 University of Kiel a Massachusetts Institute of Technology, b University of California, Berkeley, c Humboldt University ofBerlin, d Hebrew University of Jerusalem, e University of California, Los Angeles, f California Instituteof Technology, g London School of Economics, h Ludwig Maximilian University of Munich, i SapienzaUniversity of Rome, j University of Southern California, k Saint Petersburg State University, l NationalAutonomous University of Mexico, m Martin Luther University of Halle-Wittenberg, n Technical Univer-sity of Berlin, o University of North Carolina at Chapel Hill, p Technical University of Munich, q Universityof California, San Diego
Fig. 20.
Reduced Google matrix ¯ G R for PageRank top 100 universities in WRWU (top 10 is in Tab. 2, top 100 is in Tab. SI1)averaged over 24 Wikipedia editions. Matrix entries correspond to universities ordered according the top 100 WRWU PageRankorder. The full reduced Google matrix ¯ G R is presented in top left panel, ¯ G pr in top right panel, ¯ G rr in bottom left panel, and¯ G qrnd in bottom right panel. The matrix weights are W R = 1, W pr = 0 . W rr = 0 . W qr = 0 . W qrnd = 0 . another group of green universities of this time period islinked with Oxford and Cambridge and is located mainlyon US east coast (Harvard, Yale, Princeton; Columbia isdirectly linked to Cambridge). The university of next cen-turies 19th-20th, marked in black (MIT is group leader),are mainly located in US but new universities of this timeperiod appear also in Japan (Tokyo, Kyoto), Egypt (Al-Azhar), Germany (TU Munich, TU Berlin, Free Berlin)and Sweeden (Stockholm). Thus the obtained friendshipnetwork provides a compact description of world universi-ties development through 10 centuries taking into accountthe balanced view of 24 cultures presented by Wikipediaeditions. In our second division we mark universities by con-tinent location: blue for America, red for Europe, greenfor Asia (Russia is attributed to Asia), yellow for Ocea-nia and black for Africa. Again color group leaders aremarked by full circles. The friendship network obtainedfrom ¯ G rr + ¯ G qrnd is shown in Fig. 22. The network has twolarge clusters of European universities (red) and US uni-versities (blue). The group of university in Asia (green) ismainly linked between themselves having secondary linkswith Europe and US. Oceania (Sydney) and Africa (Al-Azhar) are represented only by one university. This net-work structure clearly shows the influence of European ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 15 Fig. 21.
Century reduced friendship network constructed for universities of PageRank top 100 list of WRWU (see Tab. SI1, top10 are in Tab. 2), computed from ¯ G rr + ¯ G qrnd averaged over 24 Wikipedia editions. Color marks university founded at the sametime (century) period given in years; color filled circles are time period leaders, open circles of the same color are universitiesfrom the same time period. We show 5 friendship levels (gray circles). Links originating from 1st level universities are presentedby solid lines, from 2nd level by dashed lines, from 3rd level by doted lines, and from 4th or 5th level by “ \ ” symbol lines. and US universities with emerging group of new group ofAsian universities with strong internal links. In this work we performed analysis of ranking and inter-actions of world universities from directed networks of 24Wikipedia editions dated by May 2017. Our results showthat obtained WRWU2017 with PageRank algorithm av-eraged over 24 editions gives a reliable ranking of universi- ties with 60% overlap with top 100 of ARWU2017 (Shang-hai ranking) [3]. At the same time WRWU2017 highlightsin a stronger way the significance of historical path of agiven university over centuries. There are certain changesin WRWU2017 version comparing to WRWU2013 versiondemonstrating appearance of new universities with timeevolving and with the increase of the number of Wiki-pedia articles in the 24 selected editions. A comparisonof WRWU and ARWU ranking positions for specific uni-
Fig. 22.
Continent reduced friendship network constructed for universities of PageRank top 100 list of WRWU (see Tab. SI1,top 10 are in Tab. 2), computed from ¯ G rr + ¯ G qrnd averaged over 24 Wikipedia editions. Color marks university of the samecontinent; color filled circles are continent leaders, open circles of the same color are universities from the same continent. Weobtain 5 friendship levels (gray circles). Links originating from 1st level universities are presented by solid lines, from 2nd levelby dashed lines, from 3rd level by doted lines, and from 4th or 5th level by “ \ ” symbol lines. versities (e.g. Rice University) shows that the Wikipediavisibility can be significantly improved in certain cases.We also performed an additional analysis based on thereduced Google matrix (REGOMAX) algorithm [26,27].This approach allowed us to establish direct and indirectlinks between universities and world countries. As a resultwe obtain the sensitivity and influence of specific univer-sities on world countries as it is seen by Wikipedia. TheREGOMAX method allows to perform a democratic anduniform averaging over cultural views of 24 language edi-tions and obtain a balanced cultural view on the inter-actions of top world universities through ten centuries oftheir historical development as well as their influence overcontinents.Finally we stress that the WRWU method is indepen-dent of various personal opinions being based on purelymathematical and statistical analysis of the Wikipediadatabase. We think that this approach can be very com-plimentary to ARWU and other university rankings. Wenote that Wikipedia articles of universities usually appear in the top line (or lines) of Google search. As a result theworld visibility of a given university can be publicly andfreely broadcast all over the world increasing visibility ofcertain universities. We estimate that the improvement ofWikipedia articles of certain universities (e.g. we founda low visibility of French universities) can be an efficientway to increase their world visibility, attractivity and in-fluence. Such an improvement is rather inexpensive andcan be performed by a small group of researchers and stu-dents having knowledge in languages, history, computerand network sciences. We think that this approach can becomplementary to various government projects which aimto increase visibility of national universities (like e.g. [4,5]). Acknowledgments
This work was supported by the French “Investissements d’Ave-nir” program, project ISITE-BFC (contract ANR-15-IDEX-0003) and by the Bourgogne Franche-Comt´e Region 2017-2020´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 17APEX project (conventions 2017Y-06426, 2017Y-06413, 2017Y-07534; see http://perso.utinam.cnrs.fr/~lages/apex/ ). Theresearch of DLS is supported in part by the Programme In-vestissements d’Avenir ANR-11-IDEX-0002-02, reference ANR-10-LABX-0037-NEXT (project THETRACOM).
References
1. UNESCO Liaison Office 24 July 2017, NewYork Office, Available: . Accessed July 20182. E. Hazelkorn,
Rankings and the Reshaping of Higher Ed-ucation: The Battle for World-Class Excellence , PalgraveMacmillan, New York (2015)3. Academic Ranking of World Universities. Available: . Accessed July 20184. Enseignement sup´erieur et recherche, In-vestissements d’avenir. Available: . Accessed July 20185. Russian Academic Excellence Project. Available: http://5top100.ru/ . Accessed July 20186. Times Higher Education World University Ranking. Avail-able: . AccessedJuly 20187. U-Multirank of European Union. Available: . Accessed July 20188. IREG Observatory on Academic Ranking and Excellence.Available: http://ireg-observatory.org/en/ . AccessedJuly 20189. H. J¨ons and M. Hoyler,
Global geographies of higher edu-cation: The perspective of world university rankings , Geo-forum , 45 (2013)10. A. Rauhvargers, Global University Rankings and Their Im-pact - Report II , European University Association (2013)ISBN: 978907899741211. D. Docampo and L. Cram,
On the internal dynamics ofthe Shanghai ranking , Scientometrics , 1347 (2014)12. A.O. Zhirov, O.V. Zhirov and D.L. Shepelyansky, Two-dimensional ranking of Wikipedia articles , Eur. Phys. J. B , 523 (2010)13. Y.-H. Eom, K.M. Frahm, A. Benczur and D.L. Shepelyan-sky, Time evolution of Wikipedia network ranking , Eur.Phys. J. B , 492 (2013)14. J.Lages, A.Patt and D.L.Shepelyansky, Wikipedia rankingof world universities , Eur. Phys. J. B , 69 (2016)15. Y.-H. Eom, P.Aragon, D.Laniado, A.Kaltenbrunner,S.Vigna and D.L. Shepelyansky, Interactions of culturesand top people of Wikipedia from ranking of 24 languageeditions , PLoS ONE , e0114825 (2015)16. EC FET Open project NADINE Available: . Accessed July 201817. S. Brin and L. Page,
The anatomy of a large-scale hyper-textual Web search engine , Computer Networks and ISDNSystems , 107 (1998).18. A.M. Langville and C.D. Meyer, Google’s PageRank andbeyond: the science of search engine rankings , PrincetonUniversity Press, Princeton (2006) 19. L. Ermann, K.M. Frahm and D.L. Shepelyansky,
Googlematrix analysis of directed networks , Rev. Mod. Phys. ,1261 (2015)20. L. Ermann, K.M. Frahm and D.L. Shepelyansky, Googlematrix , Scholarpedia , 30944 (2016)21. R.A. Pagel (2016) Available: http://librarylearningspace.com/ruths-rankings-17-wikipedia-google-scholar-sources-university-rankings-influence-popularity-open-bibliometrics/ . Accessed July 201822. Web page WRWU 2013, Available: http://perso.utinam.cnrs.fr/~lages/datasets/WRWU/ . Accessed July201823. G. Katz and L. Rokach,
Wikiometrics: a Wikipedia basedranking system , World Wide Web , 1153 (2017)24. K. Ban, M. Perc and Z. Levnajic,
Robust clustering of lan-guages across Wikipedia growth , R. Soc. open sci. , 171217(2017)25. K.M. Frahm and D.L. Shepelyansky, Wikipedia networksof 24 editions of 2017 , Available: . Accessed July 201826. K.M. Frahm and D.L. Shepelyansky,
Reduced Google ma-trix , arXiv:1602.02394[physics.soc] (2016)27. K.M. Frahm, K. Jaffr`es-Runser and D.L. Shepelyansky,
Wikipedia mining of hidden links between political leaders ,Eur. Phys. J. B , 269 (2016)28. S. El Zant, K.M. Frahm, K. Jaffres-Runser and D.L. She-pelyansky, Analysis of world terror networks from the re-duced Google matrix of Wikipedia , Eur. Phys. J. B , 7(2018)29. J. Lages, D.L. Shepelyansky and A. Zinovyev, nferring hid-den causal relations between pathway members using re-duced Google matrix of directed biological networks , PLoSONE , e0190812 (2018)30. Web page WRWU 2017, Available: http://perso.utinam.cnrs.fr/~lages/datasets/WRWU17/ . AccessedJuly 201831. A.D. Chepelianskii, Towards physical laws for software ar-chitecture , arXiv:1003.5455 [cs.SE] (2010)32. Country codes ISO 3166-1 alpha-2. Available: https://en.wikipedia.org/wiki/ISO_3166-1_alpha-2 . AccessedJuly 201833.
Jenks natural breaks optimization entry in English Wikipe-dia, Available https://en.wikipedia.org/wiki/Jenks_natural_breaks_optimization . Accessed June 201834. S. El Zant, K. Jaffres-Runser, K.M. Frahm and D.L. Shep-elyansky,
Interactions and influence of world painters fromthe reduced Google matrix of Wikipedia networks , PLoSONE , e0201397 (2018)35. P. Shannon, A. Markiel, O. Ozier, N.S. Baliga, J.T. Wang,D. Ramage, N. Amin, B. Schwikowski and T. Ideker,
Cytoscape: a software environment for integrated modelsof biomolecular interaction networks , Genome Research , 2498-504 (2003)8 C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks
Supplementary Information: World influence and interactions of universities from Wikipedianetworks
UKTNDOSRFOUZAESNBGPRPSBNGECRQATWGTZAJOMMSVLVGLKPCUMABDBYYECYVESKCOUYKWIQSASYNPROVNINMYLBHUCLPHIRSGTRTHLTBRGRIDRSBEARUAMXAUPTIEKRESEENOCNFIEGCHILPLDKFRCZCANLJPSEITRUATDEUS H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L A U P e nn N Y U U T A u s t i n F l o r i d a E d i n U W - M a d i s on U S C UKTNDOSRFOUZAESNBGPRPSBNGECRQATWGTZAJOMMSVLVGLKPCUMABDBYYECYVESKCOUYKWIQSASYNPROVNINMYLBHUCLPHIRSGTRTHLTBRGRIDRSBEARUAMXAUPTIEKRESEENOCNFIEGCHILPLDKFRCZCANLJPSEITRUATDEUS H a r va r d O x f o r d C a m b r i dg e C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L A U P e nn N Y U U T A u s t i n F l o r i d a E d i n U W - M a d i s on U S C Fig. SI1.
University to Country sector of the G qr matrix (left panel) and of the G rr + G qrnd composite matrix (right panel).See Fig. 5, bottom left (right) panel for the complete G rr ( G qr ) matrix. Fig. SI2.
Reduced network from G rr + G qrnd associated to the top20 ENWRWU and 240 countries listed in Tab. SI4. Foreach regional leaders, Stanford University, University of Chicago, Harvard University, University of Oxford, the four strongestlinks to one of the 240 countries are presented. Universities (countries) are represented by empty (full) nodes. The color codefor countries depends on the main spoken language: blue for English, red for Arabic, orange for Spanish, violet for Chinese, green for Hindi, yellow for Hebrew, and gray for others. Red links are purely hidden links and black ones are at least presentin the adjacency matrix.´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 19 ChicagoParis-NanterreUCLouvainMontrealULBParis-SorbonneBerkleyPrincetonPantheon-SorbonneULavalEPHEStanfordColumbiaYaleMITENSCambridgePolytechniqueOxfordHarvard H a r va r d O x f o r d P o l y t ec hn i qu e C a m b r i dg e E N S M I T Y a l e C o l u m b i a S t a n f o r d EP H E U L ava l P a n t h e on - S o r bonn e P r i n ce t on B e r k l ey P a r i s - S o r bonn e U L B M on t r ea l UC Lou va i n P a r i s - N a n t e rr e C h i ca go ChicagoParis-NanterreUCLouvainMontrealULBParis-SorbonneBerkleyPrincetonPantheon-SorbonneULavalEPHEStanfordColumbiaYaleMITENSCambridgePolytechniqueOxfordHarvard H a r va r d O x f o r d P o l y t ec hn i qu e C a m b r i dg e E N S M I T Y a l e C o l u m b i a S t a n f o r d EP H E U L ava l P a n t h e on - S o r bonn e P r i n ce t on B e r k l ey P a r i s - S o r bonn e U L B M on t r ea l UC Lou va i n P a r i s - N a n t e rr e C h i ca go Fig. SI3.
Matrices G rr (left panel) and G qrnd (right panel) for top20 FRWRWU (Tab. 6). The matrix weights are W rr = 0 . W qrnd = 0 . JenaKielMarburgCambridgeGU FrankfurtHamburgOxfordMunsterCologneFreiburgLeipzigBonnHarvardTubingenViennaFree BerlinHeidelbergGottingenHU BerlinLMU Munich L M U M un i c h HU B e r li n G o tt i ng e n H e i d e l b e r g F r ee B e r li n V i e nn a Tub i ng e n H a r va r d B onn L e i p z i g F r e i bu r g C o l ogn e M un s t e r O x f o r d H a m bu r g G U F r a n k f u r t C a m b r i dg e M a r bu r g K i e l Je n a JenaKielMarburgCambridgeGU FrankfurtHamburgOxfordMunsterCologneFreiburgLeipzigBonnHarvardTubingenViennaFree BerlinHeidelbergGottingenHU BerlinLMU Munich L M U M un i c h HU B e r li n G o tt i ng e n H e i d e l b e r g F r ee B e r li n V i e nn a Tub i ng e n H a r va r d B onn L e i p z i g F r e i bu r g C o l ogn e M un s t e r O x f o r d H a m bu r g G U F r a n k f u r t C a m b r i dg e M a r bu r g K i e l Je n a Fig. SI4.
Matrices G rr (left panel) and G qrnd (right panel) for top20 DEWRWU (Tab. 7). The matrix weights are W rr = 0 . W qrnd = 0 . BerkeleyViennaLeipzigBaumanHSEChicagoPrincetonStanfordNU KharkivKazan FUHU BerlinUKievColumbiaYaleMITCambridgeOxfordHarvardSPetersburg SUMoscow SU M o sc o w S U SP e t e r s bu r g S U H a r va r d O x f o r d C a m b r i dg e M I T Y a l e C o l u m b i a UK i ev HU B e r li n K a z a n F U NU K h a r k i v S t a n f o r d P r i n ce t on C h i ca go H SE B a u m a n L e i p z i g V i e nn a B e r ke l ey BerkeleyViennaLeipzigBaumanHSEChicagoPrincetonStanfordNU KharkivKazan FUHU BerlinUKievColumbiaYaleMITCambridgeOxfordHarvardSPetersburg SUMoscow SU M o sc o w S U SP e t e r s bu r g S U H a r va r d O x f o r d C a m b r i dg e M I T Y a l e C o l u m b i a UK i ev HU B e r li n K a z a n F U NU K h a r k i v S t a n f o r d P r i n ce t on C h i ca go H SE B a u m a n L e i p z i g V i e nn a B e r ke l ey Fig. SI5.
Matrices G rr (left panel) and G qrnd (right panel) for top20 RUWRWU (Tab. 8). The matrix weights are W rr = 0 . W qrnd = 0 . NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v Fig. SI6. G pr part of the reduced Google matrix G R for universities listed in Tab. 9 computed from EN (top left), FR (topright), DE (bottom left), and RU (bottom right) Wikipedia editions. Matrix weights are W pr (cid:39) .
956 (EN), 0 .
966 (FR), 0 . .
963 (RU).2 C´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks
NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v Fig. SI7. G rr part of the reduced Google matrix G R for universities listed in Tab. 9 computed from EN (top left), FR (topright), DE (bottom left), and RU (bottom right) Wikipedia editions. Matrix weights are W rr (cid:39) . . . . NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v NU KharkivUKievULBViennaBaumanKazan FUSPetersburg SUMoscow SUMontrealULavalEdinCambridgeOxfordJenaKielMarburgGU FrankfurtHamburgMunsterCologneFreiburgBonnTubingenFree BerlinHeidelbergGottingenLMU MunichLeipzigHU BerlinParis-NanterreParis-SorbonnePantheon-SorbonneEPHEENSPolytechniqueUSCUW-MadisonFloridaUT AustinNYUUPennUCLACornellMichiganChicagoPrincetonBerkeleyMITStanfordYaleColumbiaHarvard H a r va r d C o l u m b i a Y a l e S t a n f o r d M I T B e r ke l ey P r i n ce t on C h i ca go M i c h i g a n C o r n e ll UC L AU P e nn N Y UU T A u s t i nF l o r i d a U W - M a d i s on U S C P o l y t ec hn i qu e E N SEP H EP a n t h e on - S o r bonn e P a r i s - S o r bonn e P a r i s - N a n t e rr e HU B e r li nL e i p z i gL M U M un i c h G o tt i ng e n H e i d e l b e r gF r ee B e r li nTub i ng e n B onnF r e i bu r g C o l ogn e M un s t e r H a m bu r g G U F r a n k f u r t M a r bu r g K i e l Je n a O x f o r d C a m b r i dg e E d i n U L ava l M on t r ea l M o sc o w S U SP e t e r s bu r g S UK a z a n F UB a u m a n V i e nn a U L BUK i ev NU K h a r k i v Fig. SI8. G qr part of the reduced Google matrix G R for universities listed in Tab. 9 computed from EN (top left), FR (topright), DE (bottom left), and RU (bottom right) Wikipedia editions. Matrix weights are W qr (cid:39) . . .
015 (DE), 0 . Table SI1.
List of the first 100 universities of the 2017 Wikipedia Ranking of World Universities using PageRank algorithm.For a given university, the score Θ PR is defined by (5), N a is the number of appearances in the top 100 lists of Wikipediaeditions, CC is the country code, LC is the language code, and FC is the foundation century. Rank Θ PR N a University CC LC FC Rank Θ PR N a University CC LC FC1 2281 24 University of Oxford UK EN 11 51 464 13 University of Manchester UK EN 192 2278 24 University of Cambridge UK EN 13 52 461 11 Sapienza University of Rome IT IT 143 2277 24 Harvard University US EN 17 53 447 9 Al-Azhar University EG AR 204 2099 24 Columbia University US EN 18 54 437 8 University of Helsinki FI WR 175 1959 23 Yale University US EN 18 55 436 13 University of Minnesota US EN 196 1917 24 University of Chicago US EN 19 56 429 10 University of Illinois at Urbana–Champaign US EN 197 1858 23 Princeton University US EN 18 57 425 13 McGill University CA EN 198 1825 21 Stanford University US EN 19 58 391 5 Lund University SE SV 179 1804 21 Massachusetts Institute of Technology US EN 19 59 377 11 Georgetown University US EN 1810 1693 20 University of California, Berkeley US EN 19 60 376 10 Peking University CN ZH 1911 1578 22 Humboldt University of Berlin DE DE 19 61 351 9 University of Geneva CH DE 1612 1534 22 Cornell University US EN 19 62 349 8 Imperial College London UK EN 2013 1472 22 University of Pennsylvania US EN 18 63 347 7 University of Oslo NO WR 1914 1408 23 New York University US EN 19 64 346 8 University of Padua IT IT 1315 1395 21 University of California, Los Angeles US EN 19 65 337 13 University of Washington US EN 1916 1303 21 University of Edinburgh UK EN 16 66 331 6 Kyoto University JP JA 1917 1298 20 University of Michigan US EN 19 67 329 9 Saint Petersburg State University RU RU 1818 1221 21 Johns Hopkins University US EN 19 68 325 9 Brown University US EN 1819 1216 20 University of Vienna AT DE 14 69 308 10 University of Arizona US EN 1920 1198 20 University of G¨ottingen DE DE 18 70 306 7 Ohio State University US EN 1921 1189 21 Heidelberg University DE DE 14 71 297 7 University of Tartu EE WR 1722 1099 18 California Institute of Technology US EN 19 72 290 9 Northwestern University US EN 1923 1075 21 Moscow State University RU RU 18 73 289 5 Waseda University JP JA 1924 1031 20 University of Bologna IT IT 11 74 281 8 Boston University US EN 1925 998 19 Leipzig University DE DE 15 75 273 5 University of Warsaw PL PL 1926 993 19 Ludwig Maximilian University of Munich DE DE 15 76 263 6 ETH Zurich CH DE 1927 975 17 London School of Economics UK EN 19 77 261 6 University of Marburg DE DE 1628 891 16 Uppsala University SE SV 15 78 247 8 Martin Luther University of Halle-Wittenberg DE DE 1629 874 20 University of Southern California US EN 19 79 246 6 Michigan State University US EN 1930 851 18 University of Tokyo JP JA 19 80 241 7 University of Jena DE DE 1631 770 15 Leiden University NL NL 16 81 235 7 University of Notre Dame US EN 1932 746 13 University College London UK EN 19 82 231 6 Free University of Berlin DE DE 2033 653 15 University of Toronto CA EN 19 83 226 7 University of Salamanca ES ES 1234 651 14 Charles University CZ CS 14 84 225 6 University of Freiburg DE DE 1535 638 17 Duke University US EN 19 85 221 4 Seoul National University KR KO 2036 600 13 ´Ecole normale sup´erieure FR FR 18 86 218 5 University of Colorado Boulder US EN 1937 585 15 University of Copenhagen DK DA 15 87 215 5 Trinity College, Dublin IE EN 1638 565 11 University of Texas at Austin US EN 19 88 209 8 Indiana University US EN 1939 555 14 University of T¨ubingen DE DE 15 89 207 7 Technical University of Munich DE DE 1940 531 13 University of Bonn DE DE 19 90 207 7 University of North Carolina at Chapel Hill US EN 1841 526 15 Carnegie Mellon University US EN 19 91 206 5 University of Coimbra PT PT 1342 516 10 University of Florida US EN 19 92 204 5 Stockholm University SE SV 1943 511 12 Jagiellonian University PL PL 14 93 204 5 Utrecht University NL NL 1744 505 11 University of Glasgow UK EN 15 94 203 4 Technical University of Berlin DE DE 2045 501 11 ´Ecole polytechnique FR FR 18 95 199 3 Keio University JP JA 1946 501 13 Hebrew University of Jerusalem IL HE 20 96 199 6 University of California, San Diego US EN 2047 499 13 University of Wisconsin–Madison US EN 19 97 196 5 University of St Andrews UK EN 1548 489 9 King’s College London UK EN 16 98 196 4 University of Sydney AU EN 1949 482 14 University of Virginia US EN 19 99 195 4 University of Kiel DE DE 1750 473 15 University of Zurich CH DE 16 100 193 3 National Autonomous University of Mexico MX ES 20 ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 25
Table SI2.
List of the first 100 universities of the 2017 Academic Ranking of World Universities (ARWU). CC is the countrycode, LC is the language code, and FC is the foundation century.
Rank University CC LC FC Rank University CC LC FC1 Harvard University US EN 17 51 University of Texas at Austin US EN 192 Stanford University US EN 19 52 Vanderbilt University US EN 193 University of Cambridge UK EN 13 53 University of Maryland, College Park US EN 194 Massachusetts Institute of Technology US EN 19 54 University of Southern California US EN 195 University of California, Berkeley US EN 19 55 University of Queensland AU EN 206 Princeton University US EN 18 56 University of Helsinki FI WR 177 University of Oxford UK EN 18 57 Ludwig Maximilian University of Munich DE DE 158 Columbia University US EN 18 58 University of Zurich CH DE 169 California Institute of Technology US EN 19 59 University of Groningen NL DE 1710 University of Chicago US EN 19 60 University of Geneva CH FR 1611 Yale University US EN 18 61 University of Bristol UK EN 2012 University of California, Los Angeles US EN 19 62 University of Oslo NO WR 1913 University of Washington US EN 19 63 Uppsala University SE SV 1514 Cornell University US EN 19 64 University of California, Irvine US EN 2015 University of California, San Diego US EN 20 65 Aarhus University DK DA 2016 University College London UK EN 19 66 McMaster University CA EN 1917 University of Pennsylvania US EN 18 67 McGill University CA EN 1918 Johns Hopkins University US EN 19 68 University of Pittsburgh US EN 1819 ETH Zurich CH DE 19 69 ´Ecole Normale Sup´erieure FR FR 1820 Washington University in St. Louis US EN 19 70 Ghent University BE FR 1921 University of California, San Francisco US EN 19 71 Mayo Medical School US EN 2022 Northwestern University US EN 19 72 Peking University CN ZH 1923 University of Toronto CA EN 19 73 Erasmus University Rotterdam NL NL 2024 University of Michigan US EN 19 74 Rice University US EN 2025 University of Tokyo JP JA 19 75 Stockholm University SE SV 1926 Duke University US EN 19 76 ´Ecole Polytechnique F´ed´erale de Lausanne CH ZH 2027 Imperial College London UK EN 20 77 Purdue University US EN 1928 University of Wisconsin-Madison US EN 19 78 Monash University AU EN 2029 New York University US EN 19 79 Rutgers University US EN 1830 University of Copenhagen DK DA 15 80 Boston University US EN 1931 University of British Columbia CA EN 20 81 Carnegie Mellon University US EN 1932 University of Edinburgh UK EN 16 82 Ohio State University US EN 1933 University of North Carolina at Chapel Hill US EN 18 83 University of Sydney AU EN 1934 University of Minnesota US EN 19 84 Nagoya University JP JA 1935 Kyoto University JP JA 19 85 Georgia Institute of Technology US EN 1936 Rockefeller University US EN 20 86 Pennsylvania State University US EN 1937 University of Illinois at Urbana-Champaign US EN 19 87 University of California, Davis US EN 2038 University of Manchester UK EN 14 88 Leiden University NL NL 1639 University of Melbourne AU EN 19 89 University of Florida US EN 1940 Pierre and Marie Curie University FR FR 20 90 KU Leuven BE FR 1541 University of Paris-Sud FR FR 20 91 National University of Singapore SG ZH 2042 Heidelberg University DE DE 14 92 The University of Western Australia AU EN 2043 University of Colorado Boulder US EN 19 93 Moscow State University RU RU 1844 Karolinska Institute SE SV 19 94 Technion - Israel Institute of Technology IL HE 2045 University of California, Santa Barbara US EN 19 95 University of Basel CH ZH 1546 King’s College London UK EN 16 96 University of G¨ottingen DE DE 1847 Utrecht University NL NL 17 97 Australian National University AU EN 2048 The University of Texas Southwestern Medical Center at Dallas US EN 20 98 University of California, Santa Cruz US EN 2049 Tsinghua University CN ZH 20 99 Cardiff University UK EN 1950 Technical University of Munich DE DE 19 100 University of Arizona US EN 19
ArizonaCardiffSanta CruzAustralian NUGottingenBaselTechnionMoscow SUWestern AustraliaNU SingaporeKU LeuvenFloridaLeidenDavisPenn SUGeorgia ITNagoyaSydneyOhio SUCarnegie MellonBostonRutgersMonashPurdueEPFLStockholmRiceEURPekingMMSGhentENSPittsburghMcGillMcMasterAarhusIrvineUppsalaOsloBristolGenevaGroningenUZurichLMU MunichHelsinkiQueenslandUSCMarylandVanderbiltUT AustinTU MunichTsinghuaUT SouthwesternUtrechtKC LondonSanta BarbaraKarolinska IColorado BoulderHeidelbergParis-SudPMarie CurieMelbourneManchesterUrbana-ChampaignRockefellerKyotoMinnesotaChapel HillEdinBritish ColumbiaCopenhagenNYUUW-MadisonIC LondonDukeTokyoMichiganTorontoNorthwesternSan FranciscoWashington St. LouisETH ZurichJHopkinsUPennUC LondonSan DiegoCornellWashingtonUCLAYaleChicagoCalTecColumbiaOxfordPrincetonBerkeleyMITCambridgeStanfordHarvard H a r va r d S t a n f o r d C a m b r i dg e M I T B e r ke l ey P r i n ce t on O x f o r d C o l u m b i a C a l T ec C h i ca go Y a l e UC L A W as h i ng t on C o r n e ll S a n D i e go UC London U P e nn J H op k i n s E T H Zu r i c h W as h i ng t on S t . Lou i s S a n F r a n c i sc o N o r t h w es t e r nTo r on t o M i c h i g a nTo ky o D u ke I C London U W - M a d i s on N Y UC op e nh a g e n B r i t i s h C o l u m b i a E d i n C h a p e l H ill M i nn es o t a K y o t o R o cke f e ll e r U r b a n a - C h a m p a i gn M a n c h es t e r M e l bou r n e P M a r i e C u r i e P a r i s - S ud H e i d e l b e r g C o l o r a do B ou l d e r K a r o li n ska I S a n t a B a r b a r a KC London U t r ec h t U T S ou t h w es t e r nT s i nghu a T U M un i c h U T A u s t i n V a nd e r b il t M a r y l a nd U S C Q u ee n s l a nd H e l s i n k i L M U M un i c h U Zu r i c h G r on i ng e n G e n eva B r i s t o l O s l o U pp sa l a I r v i n e A a r hu s M c M as t e r M c G ill P i tt s bu r gh E N S G h e n t MM SP ek i ng E URR i ce S t o ck ho l m EP FL P u r du e M on as h R u t g e r s B o s t on C a r n e g i e M e ll on O h i o S U S y dn ey N a go ya G e o r g i a I T P e nn S UD av i s L e i d e nF l o r i d a KU L e u ve n NU S i ng a po r e W es t e r n A u s t r a li a M o sc o w S U T ec hn i on B ase l G o tt i ng e n A u s t r a li a n NU S a n t a C r u z C a r d i ff A r i z on a ❆(cid:0)✁✂✄☎✆❈✆(cid:0)✝✁✞✞❙✆☎✟✆❈(cid:0)✠✂❆✠✡✟(cid:0)✆☛✁✆☎☞✌●✄✟✟✁☎✍✎☎❇✆✡✎☛❚✎✏✑☎✁✄☎▼✄✡✏✄✒❙✌❲✎✡✟✎(cid:0)☎❆✠✡✟(cid:0)✆☛✁✆☞✌❙✁☎✍✆◆✄(cid:0)✎❑✌✓✎✠✔✎☎❋☛✄(cid:0)✁✝✆✓✎✁✝✎☎❉✆✔✁✡P✎☎☎❙✌●✎✄(cid:0)✍✁✆✕❚☞✆✍✄✖✆❙✖✝☎✎✖❖✑✁✄❙✌❈✆(cid:0)☎✎✍✁✎▼✎☛☛✄☎❇✄✡✟✄☎❘✠✟✍✎(cid:0)✡▼✄☎✆✡✑P✠(cid:0)✝✠✎❊P❋✓❙✟✄✏✗✑✄☛✘❘✁✏✎❊✌❘P✎✗✁☎✍▼▼❙●✑✎☎✟❊☞❙P✁✟✟✡✙✠(cid:0)✍✑▼✏●✁☛☛▼✏▼✆✡✟✎(cid:0)❆✆(cid:0)✑✠✡✕(cid:0)✔✁☎✎✌◆◆✡✆☛✆❖✡☛✄❇(cid:0)✁✡✟✄☛●✎☎✎✔✆●(cid:0)✄☎✁☎✍✎☎✌❯✠(cid:0)✁✏✑✓▼✌▼✠☎✁✏✑❍✎☛✡✁☎✗✁◗✠✎✎☎✡☛✆☎✝✌❙❈▼✆(cid:0)✖☛✆☎✝❱✆☎✝✎(cid:0)✙✁☛✟✌❚❆✠✡✟✁☎❚✌▼✠☎✁✏✑❚✡✁☎✍✑✠✆✌❚❙✄✠✟✑✒✎✡✟✎(cid:0)☎✌✟(cid:0)✎✏✑✟❑❈✓✄☎✝✄☎❙✆☎✟✆❇✆(cid:0)✙✆(cid:0)✆❑✆(cid:0)✄☛✁☎✡✗✆✕❈✄☛✄(cid:0)✆✝✄❇✄✠☛✝✎(cid:0)❍✎✁✝✎☛✙✎(cid:0)✍P✆(cid:0)✁✡✚❙✠✝P▼✆(cid:0)✁✎❈✠(cid:0)✁✎▼✎☛✙✄✠(cid:0)☎✎▼✆☎✏✑✎✡✟✎(cid:0)✌(cid:0)✙✆☎✆✚❈✑✆✘◆✆✁✍☎❘✄✏✗✎✞✎☛☛✎(cid:0)❑✖✄✟✄▼✁☎☎✎✡✄✟✆❈✑✆◆✎☛❍✁☛☛❊✝✁☎❇(cid:0)✁✟✁✡✑❈✄☛✠✘✙✁✆❈✄◆✎☎✑✆✍✎☎☞✛✌✌❲✚▼✆✝✁✡✄☎✕❈✓✄☎✝✄☎❉✠✗✎❚✄✗✖✄▼✁✏✑✁✍✆☎❚✄(cid:0)✄☎✟✄☞✄(cid:0)✟✑✒✎✡✟✎(cid:0)☎❙✆☎❋(cid:0)✆☎✏✁✡✏✄❲✆✡✑✁☎✍✟✄☎❙✟✜✓✄✠✁✡❊❚❍❯✠(cid:0)✁✏✑❏❍✄◆✗✁☎✡✌P✎☎☎✌❈✓✄☎✝✄☎❙✆☎❉✁✎✍✄❈✄(cid:0)☎✎☛☛❲✆✡✑✁☎✍✟✄☎✌❈✓❆✛✆☛✎❈✑✁✏✆✍✄❈✆☛❚✎✏❈✄☛✠✘✙✁✆❖✢✞✄(cid:0)✝P(cid:0)✁☎✏✎✟✄☎❇✎(cid:0)✗✎☛✎✖▼✕❚❈✆✘✙(cid:0)✁✝✍✎❙✟✆☎✞✄(cid:0)✝❍✆(cid:0)✔✆(cid:0)✝ ✣✤✥✦✤✥✧ ★✩✤✪✫✬✥✧ ✭✤✮✯✥✰✧✱✲ ✳✴✵ ✶✲✥✷✲✸✲✹ ✺✥✰✪✻✲✩✬✪ ✼✽✫✬✥✧ ✭✬✸✾✮✯✰✤ ✭✤✸✵✲✻ ✭✿✰✻✤✱✬ ❨✤✸✲ ❀✭❁❂ ❃✤❄✿✰✪✱✩✬✪ ✭✬✥✪✲✸✸ ★✤✪❅✰✲✱✬ ❀✭❁✬✪✧✬✪ ❀✺✲✪✪ ■✣✬▲✷✰✪❄ ❳✵✣❩✾✥✰✻✿ ❃✤❄✿✰✪✱✩✬✪★✩❬❁✬✾✰❄ ★✤✪❭✥✤✪✻✰❄✻✬ ❪✬✥✩✿❫✲❄✩✲✥✪ ✵✬✥✬✪✩✬ ✳✰✻✿✰✱✤✪ ✵✬✷✹✬ ❅✾✷✲ ✴✭❁✬✪✧✬✪ ❀❃❴✳✤✧✰❄✬✪ ❪❨❀ ✭✬▲✲✪✿✤✱✲✪ ✶✥✰✩✰❄✿✭✬✸✾✮✯✰✤ ❳✧✰✪ ✭✿✤▲✲✸✣✰✸✸ ✳✰✪✪✲❄✬✩✤ ❵✹✬✩✬ ❛✬✻✷✲✫✲✸✸✲✥ ❀✥✯✤✪✤❴✭✿✤✮▲✤✰✱✪ ✳✤✪✻✿✲❄✩✲✥ ✳✲✸✯✬✾✥✪✲ ✺✳✤✥✰✲✭✾✥✰✲ ✺✤✥✰❄❴★✾✧ ✣✲✰✧✲✸✯✲✥✱ ✭✬✸✬✥✤✧✬✶✬✾✸✧✲✥ ❵✤✥✬✸✰✪❄✷✤✴ ★✤✪✩✤✶✤✥✯✤✥✤ ❵✭❁✬✪✧✬✪ ❀✩✥✲✻✿✩ ❀✵★✬✾✩✿❫✲❄✩✲✥✪ ✵❄✰✪✱✿✾✤ ✵❀✳✾✪✰✻✿ ❀✵❂✾❄✩✰✪ ❜✤✪✧✲✥✯✰✸✩ ✳✤✥✹✸✤✪✧ ❀★✭ ❝✾✲✲✪❄✸✤✪✧ ✣✲✸❄✰✪✷✰ ❁✳❀✳✾✪✰✻✿ ❀❩✾✥✰✻✿ ❞✥✬✪✰✪✱✲✪ ❞✲✪✲✦✤ ✶✥✰❄✩✬✸ ✼❄✸✬ ❀▲▲❄✤✸✤ ✴✥✦✰✪✲ ❂✤✥✿✾❄ ✳✻✳✤❄✩✲✥ ✳✻❞✰✸✸ ✺✰✩✩❄✯✾✥✱✿ ❳❪★ ❞✿✲✪✩ ✳✳★ ✺✲✷✰✪✱ ❳❀❛ ❛✰✻✲ ★✩✬✻✷✿✬✸✮ ❳✺❭❁ ✺✾✥✧✾✲ ✳✬✪✤❄✿ ❛✾✩✱✲✥❄ ✶✬❄✩✬✪ ✭✤✥✪✲✱✰✲✳✲✸✸✬✪ ✼✿✰✬★❀ ★✹✧✪✲✹ ❪✤✱✬✹✤ ❞✲✬✥✱✰✤✴✵ ✺✲✪✪★❀ ❅✤✦✰❄ ❁✲✰✧✲✪ ❭✸✬✥✰✧✤ ❵❀❁✲✾✦✲✪ ❪❀★✰✪✱✤▲✬✥✲ ❃✲❄✩✲✥✪❂✾❄✩✥✤✸✰✤ ✳✬❄✻✬❫★❀ ✵✲✻✿✪✰✬✪ ✶✤❄✲✸ ❞✬✩✩✰✪✱✲✪ ❂✾❄✩✥✤✸✰✤✪❪❀ ★✤✪✩✤✭✥✾❡ ✭✤✥✧✰✫✫ ❂✥✰❡✬✪✤ ❢❢❣❢❤❢❣❢✐❢❣❢❥❢❣❢❦❢❣❢❧❢❣❢♠❢❣❢♥❢❣❢♦ ArizonaCardiffSanta CruzAustralian NUGottingenBaselTechnionMoscow SUWestern AustraliaNU SingaporeKU LeuvenFloridaLeidenDavisPenn SUGeorgia ITNagoyaSydneyOhio SUCarnegie MellonBostonRutgersMonashPurdueEPFLStockholmRiceEURPekingMMSGhentENSPittsburghMcGillMcMasterAarhusIrvineUppsalaOsloBristolGenevaGroningenUZurichLMU MunichHelsinkiQueenslandUSCMarylandVanderbiltUT AustinTU MunichTsinghuaUT SouthwesternUtrechtKC LondonSanta BarbaraKarolinska IColorado BoulderHeidelbergParis-SudPMarie CurieMelbourneManchesterUrbana-ChampaignRockefellerKyotoMinnesotaChapel HillEdinBritish ColumbiaCopenhagenNYUUW-MadisonIC LondonDukeTokyoMichiganTorontoNorthwesternSan FranciscoWashington St. LouisETH ZurichJHopkinsUPennUC LondonSan DiegoCornellWashingtonUCLAYaleChicagoCalTecColumbiaOxfordPrincetonBerkeleyMITCambridgeStanfordHarvard H a r va r d S t a n f o r d C a m b r i dg e M I T B e r ke l ey P r i n ce t on O x f o r d C o l u m b i a C a l T ec C h i ca go Y a l e UC L A W as h i ng t on C o r n e ll S a n D i e go UC London U P e nn J H op k i n s E T H Zu r i c h W as h i ng t on S t . Lou i s S a n F r a n c i sc o N o r t h w es t e r nTo r on t o M i c h i g a nTo ky o D u ke I C London U W - M a d i s on N Y UC op e nh a g e n B r i t i s h C o l u m b i a E d i n C h a p e l H ill M i nn es o t a K y o t o R o cke f e ll e r U r b a n a - C h a m p a i gn M a n c h es t e r M e l bou r n e P M a r i e C u r i e P a r i s - S ud H e i d e l b e r g C o l o r a do B ou l d e r K a r o li n ska I S a n t a B a r b a r a KC London U t r ec h t U T S ou t h w es t e r nT s i nghu a T U M un i c h U T A u s t i n V a nd e r b il t M a r y l a nd U S C Q u ee n s l a nd H e l s i n k i L M U M un i c h U Zu r i c h G r on i ng e n G e n eva B r i s t o l O s l o U pp sa l a I r v i n e A a r hu s M c M as t e r M c G ill P i tt s bu r gh E N S G h e n t MM SP ek i ng E URR i ce S t o ck ho l m EP FL P u r du e M on as h R u t g e r s B o s t on C a r n e g i e M e ll on O h i o S U S y dn ey N a go ya G e o r g i a I T P e nn S UD av i s L e i d e nF l o r i d a KU L e u ve n NU S i ng a po r e W es t e r n A u s t r a li a M o sc o w S U T ec hn i on B ase l G o tt i ng e n A u s t r a li a n NU S a n t a C r u z C a r d i ff A r i z on a ArizonaCardiffSanta CruzAustralian NUGottingenBaselTechnionMoscow SUWestern AustraliaNU SingaporeKU LeuvenFloridaLeidenDavisPenn SUGeorgia ITNagoyaSydneyOhio SUCarnegie MellonBostonRutgersMonashPurdueEPFLStockholmRiceEURPekingMMSGhentENSPittsburghMcGillMcMasterAarhusIrvineUppsalaOsloBristolGenevaGroningenUZurichLMU MunichHelsinkiQueenslandUSCMarylandVanderbiltUT AustinTU MunichTsinghuaUT SouthwesternUtrechtKC LondonSanta BarbaraKarolinska IColorado BoulderHeidelbergParis-SudPMarie CurieMelbourneManchesterUrbana-ChampaignRockefellerKyotoMinnesotaChapel HillEdinBritish ColumbiaCopenhagenNYUUW-MadisonIC LondonDukeTokyoMichiganTorontoNorthwesternSan FranciscoWashington St. LouisETH ZurichJHopkinsUPennUC LondonSan DiegoCornellWashingtonUCLAYaleChicagoCalTecColumbiaOxfordPrincetonBerkeleyMITCambridgeStanfordHarvard H a r va r d S t a n f o r d C a m b r i dg e M I T B e r ke l ey P r i n ce t on O x f o r d C o l u m b i a C a l T ec C h i ca go Y a l e UC L A W as h i ng t on C o r n e ll S a n D i e go UC London U P e nn J H op k i n s E T H Zu r i c h W as h i ng t on S t . Lou i s S a n F r a n c i sc o N o r t h w es t e r nTo r on t o M i c h i g a nTo ky o D u ke I C London U W - M a d i s on N Y UC op e nh a g e n B r i t i s h C o l u m b i a E d i n C h a p e l H ill M i nn es o t a K y o t o R o cke f e ll e r U r b a n a - C h a m p a i gn M a n c h es t e r M e l bou r n e P M a r i e C u r i e P a r i s - S ud H e i d e l b e r g C o l o r a do B ou l d e r K a r o li n ska I S a n t a B a r b a r a KC London U t r ec h t U T S ou t h w es t e r nT s i nghu a T U M un i c h U T A u s t i n V a nd e r b il t M a r y l a nd U S C Q u ee n s l a nd H e l s i n k i L M U M un i c h U Zu r i c h G r on i ng e n G e n eva B r i s t o l O s l o U pp sa l a I r v i n e A a r hu s M c M as t e r M c G ill P i tt s bu r gh E N S G h e n t MM SP ek i ng E URR i ce S t o ck ho l m EP FL P u r du e M on as h R u t g e r s B o s t on C a r n e g i e M e ll on O h i o S U S y dn ey N a go ya G e o r g i a I T P e nn S UD av i s L e i d e nF l o r i d a KU L e u ve n NU S i ng a po r e W es t e r n A u s t r a li a M o sc o w S U T ec hn i on B ase l G o tt i ng e n A u s t r a li a n NU S a n t a C r u z C a r d i ff A r i z on a Fig. SI9.
Reduced Google matrix G R for top100 universities in ARWU (Tab. SI1) averaged over 24 Wikipedia editions. Thefull reduced Google matrix G R is presented in top left panel, G pr in top right panel, G rr in bottom left panel, and G qrnd inbottom right panel. The matrices weights are W R = 1, W pr = 0 . W rr = 0 . W qr = 0 . Table SI3.
List of countries with corresponding country codes (CC) and language codes (LC). Only countries appearing inthe top 100 universities of the 24 considered 2017 Wikipedia editions using PageRank, CheiRank, and 2DRank algorithms arelisted here. LC is determined by the most spoken language in the given country. Country codes (CC) follow ISO 3166-1 alpha-2standard [32]. Language codes are based on language edition codes of Wikipedia; WR represents all languages other than theconsidered 24 languages.
CC Country LC CC Country LC CC Country LCAE United Arab Emirates AR GE Georgia WR NP Nepal WRAF Afghanistan FA GL Greenland DA NZ New Zealand ENAL Albania WR GR Greece EL PE Peru ESAM Armenia WR GT Guatemala ES PG Papua New Guinea ENAO Angola PT HK Hong Kong ZH PH Philippines ENAR Argentina ES HN Honduras ES PK Pakistan HIAT Austria DE HR Croatia WR PL Poland PLAU Australia EN HU Hungary HU PR Puerto Rico ESAZ Azerbaijan TR ID Indonesia WR PS State of Palestine ARBA Bosnia and Herzegovina WR IE Ireland EN PT Portugal PTBD Bangladesh WR IL Israel HE QA Qatar ARBE Belgium NL IN India HI RO Romania WRBG Bulgaria WR IQ Iraq AR RS Serbia WRBI Burundi WR IR Iran FA RU Russia RUBJ Benin FR IS Iceland WR SA Saudi Arabia ARBN Brunei MS IT Italy IT SD Sudan ARBR Brazil PT JM Jamaica EN SE Sweden SVBY Belarus RU JO Jordan AR SG Singapore ZHCA Canada EN JP Japan JA SK Slovakia WRCD Dem. Rep. of Congo FR KE Kenya EN SN Senegal FRCH Switzerland DE KG Kyrgyzstan WR SR Suriname NLCI Ivory Coast FR KH Cambodia WR SV El Salvador ESCL Chile ES KP North Korea KO SY Syria ARCN China ZH KR South Korea KO TH Thailand THCO Colombia ES KW Kuwait AR TL Timor-Leste PTCR Costa Rica ES KZ Kazakhstan WR TN Tunisia ARCU Cuba ES LA Laos WR TR Turkey TRCV Cape Verde PT LB Lebanon AR TW Taiwan ZHCY Cyprus EL LT Lithuania WR UA Ukraine WRCZ Czech Republic WR LV Latvia WR UG Uganda ENDE Germany DE LY Libya AR UK United Kingdom ENDK Denmark DA MA Morocco AR US United States ENDO Dominican Republic ES MK Macedonia WR UY Uruguay ESDZ Algeria AR MM Myanmar WR UZ Uzbekistan WREC Ecuador ES MT Malta EN VA Holy See ITEE Estonia WR MX Mexico ES VE Venezuela ESEG Egypt AR MY Malaysia MS VN Vietnam VIES Spain ES NE Niger FR YE Yemen ARFI Finland WR NG Nigeria EN ZA South Africa WRFO Faroe Islands DA NL Netherlands NL ZW Zimbabwe ENFR France FR NO Norway WR
Table SI4.
List of 240 countries and territories ranked from 2017 Wikipedia English edition using PageRank algorithm.Country codes (CC) follow ISO 3166-1 alpha-2 standard [32].
Rank Country CC Rank Country CC Rank Country CC1 United States US 81 Madagascar MG 161 Niger NE2 France FR 82 Armenia AM 162 Gabon GA3 Germany DE 83 Lebanon LB 163 Brunei BN4 United Kingdom UK 84 Cyprus CY 164 Belize BZ5 Iran IR 85 Antarctica AQ 165 Guinea GN6 India IN 86 Kazakhstan KZ 166 Chad TD7 Canada CA 87 Latvia LV 167 Malawi MW8 Australia AU 88 Panama PA 168 Togo TG9 China CN 89 Belarus BY 169 Liechtenstein LI10 Italy IT 90 Albania AL 170 United States Virgin Islands VI11 Japan JP 91 Papua New Guinea PG 171 Samoa WS12 Russia RU 92 Luxembourg LU 172 Burundi BI13 Brazil BR 93 Ghana GH 173 South Sudan SS14 Spain ES 94 United Arab Emirates AE 174 Republic of the Congo CG15 Netherlands NL 95 Uruguay UY 175 East Timor TL16 Poland PL 96 North Korea KP 176 Cape Verde CV17 Sweden SE 97 Yemen YE 177 Jersey JE18 Mexico MX 98 Costa Rica CR 178 Eritrea ER19 Turkey TR 99 Malta MT 179 Mauritania MR20 Romania RO 100 Tunisia TN 180 Central African Republic CF21 New Zealand NZ 101 Jamaica JM 181 Maldives MV22 South Africa ZA 102 Zimbabwe ZW 182 Tonga TO23 Norway NO 103 Cambodia KH 183 Andorra AD24 Switzerland CH 104 Cameroon CM 184 Vanuatu VU25 Philippines PH 105 Mongolia MN 185 State of Palestine PS26 Austria AT 106 Burkina Faso BF 186 Lesotho LS27 Belgium BE 107 Jordan JO 187 Cook Islands CK28 Pakistan PK 108 Sudan SD 188 The Gambia GM29 Argentina AR 109 Uganda UG 189 French Polynesia PF30 Indonesia ID 110 Guatemala GT 190 Swaziland SZ31 Greece GR 111 Libya LY 191 American Samoa AS32 Denmark DK 112 Greenland GL 192 Falkland Islands FK33 South Korea KR 113 Dominican Republic DO 193 Seychelles SC34 Israel IL 114 Haiti HT 194 Grenada GD35 Hungary HU 115 Moldova MD 195 San Marino SM36 Finland FI 116 Somalia SO 196 Northern Mariana Islands MP37 Egypt EG 117 Ivory Coast CI 197 Saint Lucia LC38 Portugal PT 118 Namibia NA 198 Palau PW39 Taiwan TW 119 Paraguay PY 199 Marshall Islands MH40 Ukraine UA 120 Angola AO 200 Guernsey GG41 Sri Lanka LK 121 Uzbekistan UZ 201 Equatorial Guinea GQ42 Czech Republic CZ 122 Montenegro ME 202 Dominica DM43 Malaysia MY 123 Kuwait KW 203 Cayman Islands KY44 Peru PE 124 Laos LA 204 Aruba AW45 Thailand TH 125 Mozambique MZ 205 Guinea-Bissau GW46 Hong Kong HK 126 Nicaragua NI 206 Cura¸cao CW47 Colombia CO 127 Qatar QA 207 Comoros KM48 Bulgaria BG 128 Senegal SN 208 Djibouti DJ49 Chile CL 129 Fiji FJ 209 Tuvalu TV50 Republic of Ireland IE 130 Mali ML 210 Niue NU51 Singapore SG 131 Honduras HN 211 Western Sahara EH52 Serbia RS 132 Macau MO 212 British Virgin Islands VG53 Azerbaijan AZ 133 Isle of Man IM 213 Nauru NR54 Vietnam VN 134 Zambia ZM 214 Saint Vincent & Grenadines VC55 Nepal NP 135 El Salvador SV 215 Kiribati KI56 Estonia EE 136 Bermuda BM 216 Saint Helena SH57 Croatia HR 137 Kyrgyzstan KG 217 Saint Kitts and Nevis KN58 Nigeria NG 138 Kosovo XK 218 Mayotte YT59 Afghanistan AF 139 Guyana GY 219 Micronesia FM60 Iraq IQ 140 Trinidad and Tobago TT 220 Antigua and Barbuda AG61 Bangladesh BD 141 Mauritius MU 221 Netherlands Antilles AN62 Syria SY 142 Guam GU 222 Montserrat MS63 Myanmar MM 143 Tajikistan TJ 223 S˜ao Tom´e and Pr´ıncipe ST64 Kenya KE 144 Monaco MC 224 Saint Pierre and Miquelon PM65 Slovakia SK 145 New Caledonia NC 225 Wallis and Futuna WF66 Venezuela VE 146 Oman OM 226 Turks and Caicos Islands TC67 Slovenia SI 147 Suriname SR 227 Sint Maarten SX68 Morocco MA 148 Liberia LR 228 Saint Barth´elemy BL69 Cuba CU 149 Solomon Islands SB 229 Anguilla AI70 Algeria DZ 150 Sierra Leone SL 230 Tokelau TK71 Bosnia and Herzegovina BA 151 Bhutan BT 231 Pitcairn Islands PN72 Ecuador EC 152 The Bahamas BS 232 Christmas Island CX73 Puerto Rico PR 153 Bahrain BH 233 Cocos (Keeling) Islands CC74 Saudi Arabia SA 154 Barbados BB 234 Saint Martin MF75 Lithuania LT 155 Botswana BW 235 British Indian Ocean Territory IO76 Iceland IS 156 Rwanda RW 236 Svalbard and Jan Mayen SJ77 Bolivia BO 157 Gibraltar GI 237 Georgia GE78 Tanzania TZ 158 Faroe Islands FO 238 Macedonia MK79 Ethiopia ET 159 Turkmenistan TM 239 Vatican VA80 Dem. Rep. of Congo CD 160 Benin BJ 240 Reunion RE ´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 29
Table SI5.
Universities from top100 2017 ARWU ordered according to PageRank algorithm applied to the reduced Googlematrix averaged over 24 Wikipedia editions.
Rank PageRank University Rank PageRank University1 0.0745472 Harvard University 51 0.00583189 University of Washington2 0.0621785 University of Oxford 52 0.00560402 Northwestern University3 0.0609665 University of Cambridge 53 0.00556462 University of Groningen4 0.0397826 MIT a
54 0.00545821 University of Wisconsin-Madison5 0.0355868 Columbia University 55 0.00545373 U of I, Illinois f b
58 0.00530861 University of Geneva9 0.0266544 Princeton University 59 0.00516361 Ohio State University10 0.0250087 University of Chicago 60 0.00502027 Tsinghua University11 0.0195607 University of Copenhagen 61 0.00491138 Ghent University12 0.0189782 Uppsala University 62 0.0049034 University of Arizona13 0.0176773 University of Tokyo 63 0.00473034 University of California, San Diego14 0.0165834 Moscow State University 64 0.00468699 Purdue University15 0.0148824 Cornell University 65 0.00465378 University of Basel16 0.0145334 University of Pennsylvania 66 0.0046221 UNC Chapel Hill g
17 0.0141382 UCLA c
67 0.00455207 Technical University of Munich18 0.0131496 New York University 68 0.00444405 University of Sydney19 0.0131307 California Institute of Technology 69 0.00437431 University of Maryland, College Park20 0.0125402 University G¨ottingen 70 0.00430464 Rutgers University21 0.0124228 Leiden University 71 0.00404074 Karolinska Institute22 0.0124135 Heidelberg University 72 0.0039799 University of Pittsburgh23 0.012155 University of Edinburgh 73 0.00396299 Georgia Institute of Technology24 0.0115044 University of Michigan 74 0.00385092 Penn State University25 0.0107339 Johns Hopkins University 75 0.00369518 Washington University in St. Louis26 0.0105176 University of Munich d
76 0.00364923 University of British Columbia27 0.00917197 University College London 77 0.00360777 Australian National University28 0.00872849 Duke University 78 0.00355039 University of California, Santa Barbara29 0.00819352 University of Southern California 79 0.00352429 University of Bristol30 0.00814739 ETH Zurich 80 0.00337135 National University of Singapore31 0.00802171 Kyoto University 81 0.00326108 Rockefeller University32 0.00797102 Aarhus University 82 0.00320465 Rice University33 0.00795232 University of Colorado Boulder 83 0.00311399 University of Melbourne34 0.00783698 ´Ecole Normale Sup´erieure 84 0.00307731 Vanderbilt University35 0.00766772 Peking University 85 0.00290042 Erasmus University Rotterdam36 0.0076523 Stockholm University 86 0.00284488 University of California, Davis37 0.00744185 University Toronto 87 0.00279911 EPFL h
38 0.0070079 University of Texas at Austin 88 0.00273436 Pierre and Marie Curie University39 0.00685167 Imperial College London 89 0.00272264 Nagoya University40 0.00681529 Utrecht University 90 0.00265046 University of California, Irvine41 0.00658785 University of Minnesota 91 0.00263142 University of Queensland42 0.00654586 Carnegie Mellon University 92 0.00210331 University of California, San Francisco43 0.00653689 University of Helsinki 93 0.0021006 Monash University44 0.00651107 KU Leuven 94 0.00198778 University of California, Santa Cruz45 0.0064442 King’s College London 95 0.00189623 Cardiff University46 0.00639753 University of Zurich 96 0.00186566 McMaster University47 0.00623053 McGill University 97 0.00186277 University of Paris-Sud48 0.00621359 University of Manchester 98 0.00157434 The University of Western Australia49 0.00602113 University of Florida 99 0.0011675 UT Southwestern i
50 0.00600767 Technion e
100 0.00102057 Mayo Medical School a Massachusetts Institute of Technology, b University of California, Berkeley, c University of California, Los Angeles, d Ludwig Max-imilian University of Munich, e Technion - Israel Institute of Technology, f University of Illinois Urbana-Champaign, g Universityof North Carolina at Chapel Hill, h ´Ecole Polytechnique F´ed´erale de Lausanne, i The University of Texas Southwestern MedicalCenter at Dallas
Fig. SI10.
Reduced network constructed for universities listed in Tab. SI5 computed from G rr + G qrnd averaged over 24Wikipedia editions. Color filled nodes are time period leaders. We obtain 4 friendship levels with corresponding links: blacksolid lines (level 1), dashed lines (level 2), doted lines (level 3) and “ \ ” symbol lines (4+).´elestin Coquid´e et al.: World influence and interactions of universities from Wikipedia networks 31 Fig. SI11.
Reduced network constructed for universities listed in Tab. SI5 computed from G rr + G qrnd averaged over 24Wikipedia editions. Color filled nodes are continent leaders. We obtain 4 friendship levels with corresponding links: black solidlines (level 1), dashed lines (level 2), doted lines (level 3) and “ \\