An algorithm for ranking the nodes of multiplex networks with data based on the PageRank concept

Abstract

A new algorithm for attributed multiplex networks is proposed and analysed with the main objective to compute the centrality of the nodes based on the original PageRank model used to establish a ranking in the Web pages network. Taking as a basis the Adapted PageRank Algorithm for monoplex networks with data and the two-layer PageRank approach, an algorithm for biplex networks is designed with two main characteristics. First, it solves the drawback of the existence of isolated nodes in any of the layers. Second, the algorithm allows us to choose the value of the parameter α controlling the importance assigned to the network topology and the data associated to the nodes in the Adapted PageRank Algorithm, respectively. The proposed algorithm inherits this ability to determine the importance of node attribute data in the calculation of the centrality; yet, going further, it allows to choose different α values for each of the two layers. The biplex algorithm is then generalised to the case of multiple layers, that is, for multiplex networks. Its possibilities and characteristics are demonstrated using a dataset of aggregate origin-destination flows of private cars in Rome. This dataset is augmented with attribute data describing city locations. In particular, a biplex network is constructed by taking the data about car mobility for layer 1. Layer 2 is generated from data describing the local bus transport system. The algorithm establishes the most central locations in the city when these layers are intertwined with the location attributes in the biplex network. Four cases are evaluated and compared for different values of the parameter that modulates the importance of data in the network.