Abstract
Social networks are widespread and important in our daily life. Finding communities and reveal node characteristics in community are crucial to understand the network structure and function. Many methods based on Nonnegative matrix factorization (NMF) are proposed to find communities, while these results appear uncertain with the initial condition especially in weighted directed network. In this paper, firstly we improve the nonnegative matrix factorization (NMF) method with modeling network as the weighted directed graph and using diagonally dominant matrix as constraint condition to obtain the community membership of each node as well as the interaction among communities. Furthermore, we raise methods to evaluate nodes importance and to discuss node characteristics in community to analyze the network structure. Some experiments on the Zachary club datasets and other real-world datasets have been did to demonstrate the superiority of our methods for community discovery over other related matrix factorization methods. The results demonstrate that our methods are useful and applicable both in weighted directed model and undirected model for community discovery, and the results are more reliable. Experiments also illustrate the meaningful results by discussing the node characteristics in community. All those provide a useful way for analyzing social network.