| Summary: | Centrality of nodes is very useful for understanding the behavior of systems and has recently attracted plenty of attention from researchers. In this paper, we propose a new eigenvector centrality based on node similarity for ranking nodes in multilayer and temporal networks under the framework of tensor computation, referred to as the ECMSim. We define a fourth-order tensor to represent the multilayer and temporal networks. The relationships between different layers(or time stamps) can be depicted by using node similarity. Based on the defined tensor, we establish the tensor equation to obtain nodes centrality values. The nodes centrality values also can be viewed as the Perron eigenvector of a multi-homogeneous map. Furthermore, we show the existence and uniqueness of the proposed centrality measure by existing results. Numerical experiments are carried out to demonstrate that the proposed centrality outperforms some existing ranking methods.
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