A variational approach to detect communities in weighted networks

Community detection is an essential aspect in studying network structures. Most community detection methods focus on binary networks, which ignore valuable information in the edge weights. In this study, we propose a novel weighted stochastic block model (WSBM). In the proposed model, we employ the variational EM algorithm to estimate the model parameters, and then extract the community structure of the weighted network. The detection accuracy and efficiency of the proposed algorithm are demonstrated through both synthetic and real examples. The theoretical results of the proposed method in terms of the asymptotic consistency of estimating the model parameters and community structure are established. The proposed method provides an effective way to detect communities in weighted networks, with promising potential for practical applications.