Universality of the stochastic block model

TL;DR

This paper demonstrates that the stochastic block model (SBM) is nearly universal for mesoscopic pattern extraction in complex networks, unifying many algorithms under a maximum likelihood framework.

Contribution

It establishes the theoretical equivalence of popular mesoscopic pattern extraction algorithms to the SBM, highlighting its broad applicability.

Findings

Most MPE algorithms are special cases of SBM maximum likelihood.

SBM provides a unifying framework for community detection, core-periphery, and graph coloring.

SBM's universality simplifies understanding of network inference methods.

Abstract

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, and imperfect graph coloring. 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 (SBM), or one of its direct generalizations. These equivalence relations show that the SBM is nearly universal with respect to MPE problems.