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.Comment: Allerton Conference 202