Co-Ranking for nodes, layers and timestamps in multilayer temporal networks

Abstract

Understanding the structure of multilayer temporal networks requires the evaluation of nodes importance, the relationship between them and the timestamps simultaneously. In this paper,we propose a parameters-free centrality algorithm referred to as Co-Rank. The proposed algorithm uses a sixth-order tensor to describe the multilayer temporal network which considers the inter-layer connections between the adjacent timestamps across different layers. After describing the multilayer temporal network, the next step is to build and solve a set of tensor equations following the mutual relationships to get the centrality. The existence of the centrality metric is formally proven, and the convergence of the Co-Rank is also shown so that it can be effectively applied for the ranking. The results of experiments on synthetic and real-world networks show the effectiveness of our proposed algorithm.