Nodes and layers PageRank centrality for multilayer networks**Project supported by the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. AE91313/001/016), the National Natural Science Foundation of China (Grant No. 11701097), and the Natural Science Foundation of Jiangxi Province, China (Grant No. 20161BAB212055).

Abstract

In this paper, we propose a new centrality algorithm that can simultaneously rank the nodes and layers of multilayer networks, referred to as the MRFNL centrality. The centrality of nodes and layers are obtained by developing a novel iterative algorithm for computing a set of tensor equations. Under some conditions, the existence and uniqueness of this centrality were proven by applying the Brouwer fixed point theorem. Furthermore, the convergence of the proposed iterative algorithm was established. Finally, numerical experiments on a simple multilayer network and two real-world multilayer networks (i.e., Pierre Auger Collaboration and European Air Transportation Networks) are proposed to illustrate the effectiveness of the proposed algorithm and to compare it to other existing centrality measures.