Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications

TLDR

The study extends prior work on the stochastic block model to address community detection from network topology. The authors employ the cavity method to derive an exact phase diagram, characterize detectability and easy‑hard transitions, and develop a belief‑propagation algorithm that optimally infers node group memberships and learns model parameters. The algorithm is tested on two real‑world networks, demonstrating its practical performance.

Abstract

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability-undetectability phase transition and the easy-hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.