A new centrality ranking method for multilayer networks

There are a good deal of centrality ranking evaluation methods for single-layer networks. However, the centrality evaluation method of a single-layer network cannot guarantee the accuracy of the measurement results on a multilayer network. Most of the existing methods for node centrality in multilayer networks ignore the effect of network interlayer relationships on the importance of nodes. Thereby, the problem of missing information between layers of multilayer networks occurs in the calculation process, resulting in inaccurate assessment results or differences between nodes that are too small to determine their significance. This paper proposes a new centrality measure for multilayer networks, which measures the importance of nodes by calculating the weighted local structure entropy of nodes. The proposed method not only considers the importance of connections within node layers, but also adds the influence of the number of network layers between node layers. Through the empirical analysis of real multilayer networks of different types and sizes, such as the Hubei transportation multilayer network, Lazega-Law-Firm multilayer network, CS-Aarhus multilayer network, CKM-Physicians-Innovation multilayer network, it is proved that the proposed method is optimal and general.