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arXiv · 2203.15736

Exact Community Recovery in Correlated Stochastic Block Models

Julia Gaudio·Miklos Z. Racz·Anirudh Sridhar
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Abstract

We consider the problem of learning latent community structure from multiple correlated networks. We study edge-correlated stochastic block models with two balanced communities, focusing on the regime where the average degree is logarithmic in the number of vertices. Our main result derives the precise information-theoretic threshold for exact community recovery using multiple correlated graphs. This threshold captures the interplay between the community recovery and graph matching tasks. In particular, we uncover and characterize a region of the parameter space where exact community recovery is possible using multiple correlated graphs, even though (1) this is information-theoretically impossible using a single graph and (2) exact graph matching is also information-theoretically impossible. In this regime, we develop a novel algorithm that carefully synthesizes algorithms from the community recovery and graph matching literatures.

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Julia Gaudio, Miklos Z. Racz, Anirudh Sridhar. 2022-03-29. Exact Community Recovery in Correlated Stochastic Block Models. https://arxiv.org/abs/2203.15736

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