A New Centrality Measure Based on Topologically Biased Random Walks for Multilayer Networks

Abstract

In this paper, we propose a new multirank method based on topologically biased random walks for simultaneously ranking the nodes and layers in multilayer networks, referred to as the topologically biased random walks (TBRW) centrality. The centrality of nodes and layers are obtained by developing an iterative algorithm for solving a set of tensor equations. Under some conditions, the existence of such centrality is also proven. Furthermore, the convergence of the proposed iterative algorithm is established. Numerical experiments on two real-world multilayer networks (i.e., multiplex citation network and European Air Transportation Networks) are carried out to show the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.