Improved centrality measure based on the adapted PageRank algorithm for urban transportation multiplex networks

An increasing number of studies have attempted to build a multiplex network (MN) model to generalize the traditional network theory and have proposed various centrality measures for MNs. In this paper, we proposed an improved centrality measure, the Adaptive PageRank Algorithm Modified by the Gravity Model (APAMGM), to identify critical nodes in MNs. We modified the idea that the transition probability of a node is only related to its outgoing connections (or degree in an undirected network) in the adapted PageRank algorithm. In APAMGM, the transition probability is positively correlated with the quality of nodes and inversely correlated with the interaction impedance between nodes. We conducted a case study using a multiplex urban transportation network in Shenzhen, China, which consists of a bus, metro, taxi, and shared bike network. The results show that APAGMG can identify critical nodes with good interpretability and it displays potential for application in networks where spatial interactions exist between nodes. The interdependencies in the network were explored and discussed with the characterization of nodes. This study might provide insights into applying complex network theory and centrality measures to some MNs, especially urban transportation networks. •An improved centrality measure for multiplex networks is proposed.•The modification allows the identification of nodes with active features or close proximity.•The method shows potential for node identification in multiplex networks where nodes have spatial interactions.•The method can identify the most critical areas in urban public transport systems.