Eigenvector-based centralities for multilayer temporal networks under the framework of tensor computation

Abstract

In recent years, many centralities have been developed to identify the key nodes in multilayer and temporal networks. Among these centrality measures, eigenvector-based centralities are very efficient ranking algorithms. In the real world, some complex systems have multilayer structure and edges are dynamic, i.e., they appear and disappear over time, referred to as the multilayer temporal networks. Moreover, some eigenvector-based centralities have been extended to rank the nodes in multilayer temporal networks. However, these existing eigenvector-based centralities ignore the inter-layer interactions between different time stamps and may get incorrect ranking results of nodes. In order to better describe the multilayer and temporal features of networks, in this paper, we construct a sixth-order tensor to represent multilayer temporal networks. In particular, cosine similarity is used to depict the relationships of inter-layer. Then, we propose multilayer temporal eigenvector and PageRank centralities based on the sixth-order tensor and cosine similarity for ranking the nodes, layers and time stamps in networks, referred to as MTEIGBC and MTPRBC centralities. Furthermore, the existence and uniqueness of our centrality measures can be guaranteed under very reasonable conditions. Finally, numerical experiments on three networks are performed to demonstrate the effectiveness and superiority of our proposed ranking methods.