Taras Agryzkov

An algorithm for ranking the nodes of an urban network based on the concept of PageRank vector

Abstract This paper presents a new method to establish a ranking of nodes in an urban network. In the original PageRank algorithm, a single PageRank vector is computed to determine the relative importance of Web pages, independent of any particular search query. We follow a similar reasoning, adapting the concept of PageRank vector to urban networks. We translate an urban network to graph theory language, where the nodes represent crossings or squares and the edges represent the connections between nodes. In this scenario, our main goal is to establish a ranking of importance of the different nodes in the graph. Unlike the PageRank model which only takes into account the connections between the Web pages, in our method we must consider other external factors to carry out the classification. These external factors may have some characteristics associated with the nodes and they are different according to the problem we are working. These characteristics are usually related to the presence of some facilities or endowments in the nodes of the network, like for example the presence of restaurants, bars, shopping centers, stores, and so on. A data matrix will collect the quantification of each of the characteristics studied for each node and will play an important role in the process of classification. Considering the influence of all these characteristics, we construct a matrix with some interesting algebraic features which allow us to compute an eigenvector associated to the dominant eigenvalue λ = 1 . This vector constitutes the solution to our problem of ranking the nodes of the network. The model is applied to a real example, in which we consider a part (the old town) of the city of Murcia (Spain). For this example, we apply the PageRank model, as well as the proposed model in this paper, in order to perform a comparative study of both models. This example clearly shows the importance of considering external factors to quantify the urban network nodes.

A new betweenness centrality measure based on an algorithm for ranking the nodes of a network

Abstract We propose and discuss a new centrality index for urban street patterns represented as networks in geographical space. This centrality measure, that we call ranking-betweenness centrality, combines the idea behind the random-walk betweenness centrality measure and the idea of ranking the nodes of a network produced by an adapted PageRank algorithm. We initially use a PageRank algorithm in which we are able to transform some information of the network that we want to analyze into numerical values. Numerical values summarizing the information are associated to each of the nodes by means of a data matrix. After running the adapted PageRank algorithm, a ranking of the nodes is obtained, according to their importance in the network. This classification is the starting point for applying an algorithm based on the random-walk betweenness centrality. A detailed example of a real urban street network is discussed in order to understand the process to evaluate the ranking-betweenness centrality proposed, performing some comparisons with other classical centrality measures.

New highlights and a new centrality measure based on the Adapted PageRank Algorithm for urban networks

A centrality measure, with a practical application in urban network, has been proposed.The measure establishes a ranking of nodes focused on the topological data distribution.The amount of data associated with the nodes of the network has a great importance.The topology of the network and the information associated to the nodes are involved. The Adapted PageRank Algorithm (APA) proposed by Agryzkov etźal. provides us a method to establish a ranking of nodes in an urban network. We can say that it constitutes a centrality measure in urban networks, with the main characteristic that is able to consider the importance of data obtained from the urban networks in the process of computing the centrality of every node. Starting from the basic idea of this model, we modify the construction of the matrix used for the classification of the nodes in order of importance. In the APA model, the data matrix is constructed from the original idea of PageRank vector, given an equal chance to jump from one node to another, regardless of the topological distance between nodes. In the new model this idea is questioned. A new matrix with the data network is constructed so that now the data from neighboring nodes are considered more likely than data from the nodes that are farther away. In addition, this new algorithm has the characteristic that depends on a parameter α, which allows us to decide the importance attached, in the computation of the centrality, to the topology of the network and the amount of data associated with the node. Various numerical experiments with a network of very small size are performed to test the influence of the data associated with the nodes, depending always on the choice of the parameter α. Also we check the differences between the values produced by the original APA model and the new one. Finally, these measures are applied to a real urban network, in which we perform a visual comparison of the results produced by the various measures calculated from the algorithms studied.

Measuring urban activities using Foursquare data and network analysis: a case study of Murcia Spain

ABSTRACT Among social networks, Foursquare is a useful reference for identifying recommendations about local stores, restaurants, malls or other activities in the city. In this article, we consider the question of whether there is a relationship between the data provided by Foursquare regarding users’ tastes and preferences and fieldwork carried out in cities, especially those connected with business and leisure. Murcia was chosen for case study for two reasons: its particular characteristics and the prior knowledge resulting from the fieldwork. Since users of this network establish, what may be called, a ranking of places through their recommendations, we can plot these data with the objective of displaying the characteristics and peculiarities of the network in this city. Fieldwork from the city itself gives us a set of facilities and services observed in the city, which is a physical reality. An analysis of these data using a model based on a network centrality algorithm establishes a classification or ranking of the nodes that form the urban network. We compare the data extracted from the social network with the data collected from the fieldwork, in order to establish the appropriateness in terms of understanding the activity that takes place in this city. Moreover, this comparison allows us to draw conclusions about the degree of similarity between the preferences of Foursquare users and what was obtained through the fieldwork in the city.

Analyzing the commercial activities of a street network by ranking their nodes: a case study in Murcia, Spain

Urban researchers and planners are often interested in understanding how economic activities are distributed in urban regions, what forces influence their special pattern and how urban structure and functions are mutually dependent. In this paper, we want to show how an algorithm for ranking the nodes in a network can be used to understand and visualize certain commercial activities of a city. The first part of the method consists of collecting real information about different types of commercial activities at each location in the urban network of the city of Murcia, Spain. Four clearly differentiated commercial activities are studied, such as restaurants and bars, shops, banks and supermarkets or department stores, but obviously we can study other. The information collected is then quantified by means of a data matrix, which is used as the basis for the implementation of a PageRank algorithm which produces a ranking of all the nodes in the network, according to their significance within it. Finally, we visualize the resulting classification using a colour scale that helps us to represent the business network.

A Model to Visualize Information in a Complex Streets' Network

This paper discusses a process to graphically view and analyze information obtained from a network of urban streets, using an algorithm that establishes a ranking of importance of the nodes of the network itself. The basis of this process is to quantify the network information obtained by assigning numerical values to each node, representing numerically the information. These values are used to construct a data matrix that allows us to apply a classification algorithm of nodes in a network in order of importance. From this numerical ranking of the nodes, the process finish with the graphical visualization of the network. An example is shown to illustrate the whole process.

Analysing successful public spaces in an urban street network using data from the social networks Foursquare and Twitter

This paper analyzes success public spaces (specifically plazas) in the urban fabric of the city of Murcia, Spain. Two approaches were adopted. Firstly, the city was visualized as a complex network whose nodes represent plazas. A centrality algorithm was applied to determine the importance of each node. Secondly, data sets were used from social networks Foursquare and Twitter, which provide different types of data as well as user profiles. Foursquare data indicates user preferences of urban public spaces, while in this respect Twitter offers less specific user generated data. Both perspectives have facilitated two rankings based on the most visited plazas in the city. The results enabled a comparative study to determine the potential differences or similarities between both approaches.

An algorithm to compute data diversity index in spatial networks

Abstract Diversity is an important measure that according to the context, can describe different concepts of general interest: competition, evolutionary process, immigration, emigration and production among others. It has been extensively studied in different areas, as ecology, political science, economy, sociology and others. The quality of spatial context of the city can be gauged through this measure. The spatial context with its corresponding dataset can be modelled using spatial networks. Consequently, this allows us to study the diversity of data present in this specific type of networks. In this paper we propose an algorithm to measure diversity in spatial networks based on the topology and the data associated to the network. In the experiments developed with networks of different sizes, it is observed that the proposed index is independent of the size of the network, but depends on its topology.

Quantification and Visualization of a Heritage Conservation in a Quito Neighbourhood (Ecuador)

This paper focuses on the process of quantification and visualization of a heritage conservation study in a neighbourhood of Quito (Ecuador). The first part of the paper consists of collecting real information about different features of every building in the urban network of the mentioned neighbourhood. The information collected is then quantified by means of a data matrix that allows us to obtain an indicator of the heritage conservation of every parcel studied. In order to better understand the preservation of the neighbourhood, an analysis and visualization of the obtained indicators is carried out. The visualization is based on a non-linear interpolation of the vertices of a grid using a chromatic scale. This type of visualization provides a smooth graphic that helps us to represent areas that are more or less interesting from the point of view of the heritage conservation state.

Different Types of Graphs to Model a City

This work was partially supported by the Spanish Government, Ministerio de Economia y Competividad, which reference number is TIN2014-53855-P.