A semidefinite program for unbalanced multisection in the stochastic block model

TL;DR

This paper introduces a semidefinite programming algorithm for community detection in the stochastic block model, capable of exactly recovering communities of varying sizes and robust against semirandom perturbations, extending prior methods.

Contribution

The paper presents a novel SDP-based algorithm that achieves exact community recovery in unbalanced multisection stochastic block models, surpassing previous approaches in robustness and generality.

Findings

Achieves exact recovery up to information-theoretic limits.

Handles multiple communities with different sizes.

Proves robustness against semirandom model variants.

Abstract

We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure. We prove that our algorithm achieves exact recovery of the latent communities, up to the information-theoretic limits determined by Abbe and Sandon (2015). Our result extends prior SDP approaches by allowing for many communities of different sizes. By virtue of a semidefinite approach, our algorithms succeed against a semirandom variant of the stochastic block model, guaranteeing a form of robustness and generalization. We further explore how semirandom models can lend insight into both the strengths and limitations of SDPs in this setting.