{"ID":2824560,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.22773","arxiv_id":"2512.22773","title":"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.","short_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 prob...","url_abs":"https://arxiv.org/abs/2512.22773","url_pdf":"https://arxiv.org/pdf/2512.22773v1","authors":"[\"Julia Gaudio\",\"Andrew Jin\"]","published":"2025-12-28T04:30:32Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}