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

TL;DR

This paper provides an asymptotic analysis of the stochastic block model using the cavity method, revealing phase transitions in community detectability and proposing an optimal belief propagation algorithm with real-world applications.

Contribution

It extends previous work by analyzing phase transitions in the stochastic block model and develops an optimal inference algorithm based on the cavity method.

Findings

Identifies phase transitions in community detectability.

Develops a belief propagation algorithm for optimal group inference.

Demonstrates algorithm performance on real-world networks.

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.