{"paper":{"title":"Information-theoretic thresholds for community detection in sparse networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.CC","cs.IT","cs.SI","math.IT"],"primary_cat":"math.PR","authors_text":"Cristopher Moore, Jess Banks, Joe Neeman, Praneeth Netrapalli","submitted_at":"2016-07-06T19:42:06Z","abstract_excerpt":"We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, consider the symmetric stochastic block model with $q$ groups, average degree $d$, and connection probabilities $c_\\text{in}/n$ and $c_\\text{out}/n$ for within-group and between-group edges respectively; let $\\lambda = (c_\\text{in}-c_\\text{out})/(qd)$. We show that, when $q$ is large, and $\\lambda = O(1/q)$, the critical value of $d$ at which community detection becomes possible---in physical terms, the condensation threshold---is \\[ d_\\text{c} = \\Theta\\!\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01760","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}