Graph Matching in Correlated Stochastic Block Models for Improved Graph Clustering

We consider community detection from multiple correlated graphs sharing the same community structure. The correlated graphs are generated by independent subsampling of a parent graph sampled from the stochastic block model. The vertex correspondence between the correlated graphs is assumed to be unknown. We consider the two-step procedure where the vertex correspondence between the correlated graphs is first revealed, and the communities are recovered from the union of the correlated graphs, which becomes denser than each single graph. We derive the information-theoretic limits for exact graph matching in general density regimes and the number of communities, and then analyze the regime of graph parameters, where one can benefit from the matching of the correlated graphs in recovering the latent community structure of the graphs.