A Community-Based Centrality Measure for Identifying Key Nodes in Multilayer Networks

The identification of important nodes (vertexes) in multilayer networks has aroused many scholars' attention and various centrality methods have deen developed. However, the current centralities ignore the impact of community structure on node importance. In this article, we define a community-based centrality for finding key vertexes in multilayer networks, referred to as the CBCM. We first construct a multilayer network model with interlayer edges, which is represented by a fourth-order tensor. Based on the fourth-order tensor, we develop a centrality, called PR_BIS, to measure the importance of vertexes and network layers in multilayer networks, simultaneously. CBCM determines the importance of a vertex in each network layer by combining the following three factors: the PageRank centrality score of the vertex, the importance of the community where the vertex is located, and the ability of the vertex within a community to affect vertexes in other communities within two steps. Based on the importance of all the network layers measured by PR_BIS centrality, we perform weighted fusion for the importance of a vertex in all network layers to obtain the importance of the vertex in multilayer networks. Finally, numerical experiments are performed on several multilayer networks to verify the effectiveness and superiority of CBCM and PR_BIS.