Exact Recovery in the Geometric SBM

Abstract: Community detection is the problem of identifying dense communities in networks. Motivated by transitive behavior in social networks ("thy friend is my friend"), an emerging line of work considers spatially-embedded networks, which inherently produce graphs containing many triangles. In this paper, we consider the problem of exact label recovery in the Geometric Stochastic Block Model (GSBM), a model proposed by Baccelli and Sankararaman as the spatially-embedded analogue of the well-studied Stochastic Block Model. Under mild technical assumptions, we completely characterize the information-theoretic threshold for exact recovery, generalizing the earlier work of Gaudio, Niu, and Wei.