On the universality of the stochastic block model

Mesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including for instance: community detection, core-periphery identification, imperfect graph colouring. In this paper, we show that the most popular algorithms designed to solve MPE problems can in fact be understood as special cases of the maximum likelihood formulation of the stochastic block model, or one of its direct generalizations. These equivalence relations show that the SBM is nearly universal with respect to MPE problems.