关键词: 复杂网络, 中心性, 对称非负矩阵分解

Abstract: One of the most important problems in complex networks is to identify the influential vertices for understanding and controlling of information diffusion and disease spreading. Most of the current centrality algorithms focus on single feature or manually extract the attributes, which occasionally results in the failure to fully capture the vertex’s importance. A new vertex centrality approach based on symmetric nonnegative matrix factorization (SNMF), called VCSNMF, is proposed in this paper. For highlight the characteristics of a network,the adjacency matrix and the degree matrix are fused to represent original data of the network via a weighted linear combination. First, SNMF automatically extracts the latent characteristics of vertices by factorizing the established original data matrix. Then we prove that each vertex’s composite feature which is constructed with one-dimensional factor matrix can be approximated as the term of eigenvector associated with the spectral radius of the network, otherwise obtained by the factor matrix on the hyperspace. Finally, VCSNMF integrates the composite feature and the topological structure to evaluate the performance of vertices. To verify the effectiveness of the VCSNMF criterion, eight existing centrality approaches are used as comparison measures to rank influential vertices in ten real-world networks. The experimental results assert the superiority of the method.