  We propose a generalized stochastic block model to explore the mesoscopic
structures in signed networks by grouping vertices that exhibit similar
positive and negative connection profiles into the same cluster. In this model,
the group memberships are viewed as hidden or unobserved quantities, and the
connection patterns between groups are explicitly characterized by two block
matrices, one for positive links and the other for negative links. By fitting
the model to the observed network, we can not only extract various structural
patterns existing in the network without prior knowledge, but also recognize
what specific structures we obtained. Furthermore, the model parameters provide
vital clues about the probabilities that each vertex belongs to different
groups and the centrality of each vertex in its corresponding group. This
information sheds light on the discovery of the networks' overlapping
structures and the identification of two types of important vertices, which
serve as the cores of each group and the bridges between different groups,
respectively. Experiments on a series of synthetic and real-life networks show
the effectiveness as well as the superiority of our model.
