Community Detection in the Labelled Stochastic Block Model

TL;DR

This paper investigates community detection in labeled stochastic block models with multiple interaction types, identifying a critical threshold for successful reconstruction and validating it through theoretical proofs and numerical experiments.

Contribution

It conjectures and provides evidence for a threshold in community detection in labeled SBMs, linking belief propagation behavior and inference feasibility.

Findings

Belief propagation transition from insensitive to sensitive at the threshold

Transition from infeasible to feasible inference on the tree model

Numerical results support the conjectured threshold

Abstract

We consider the problem of community detection from observed interactions between individuals, in the context where multiple types of interaction are possible. We use labelled stochastic block models to represent the observed data, where labels correspond to interaction types. Focusing on a two-community scenario, we conjecture a threshold for the problem of reconstructing the hidden communities in a way that is correlated with the true partition. To substantiate the conjecture, we prove that the given threshold correctly identifies a transition on the behaviour of belief propagation from insensitive to sensitive. We further prove that the same threshold corresponds to the transition in a related inference problem on a tree model from infeasible to feasible. Finally, numerical results using belief propagation for community detection give further support to the conjecture.