A generalized stochastic block model for overlapping community detection

Over the past two decades, community detection has been extensively explored. Yet, the problem of identifying overlapping communities has not been fully solved. In this paper, we introduce a novel approach, called the generalized stochastic block model, to address this issue by allowing nodes to belong to multiple communities. This approach extends the traditional representation of nodal community assignment from a single community label to a label vector, with each element indicating the membership of a node in a specific community. We develop a Markov chain Monte Carlo algorithm to tackle the model. Through numerical experiments conducted on synthetic and empirical networks, we demonstrate the efficacy of the proposed framework in accurately detecting overlapping communities.