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.