{"paper":{"title":"Asymptotic Mutual Information for the Two-Groups Stochastic Block Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Emmanuel Abbe, Yash Deshpande","submitted_at":"2015-07-30T20:56:38Z","abstract_excerpt":"We develop an information-theoretic view of the stochastic block model, a popular statistical model for the large-scale structure of complex networks. A graph $G$ from such a model is generated by first assigning vertex labels at random from a finite alphabet, and then connecting vertices with edge probabilities depending on the labels of the endpoints. In the case of the symmetric two-group model, we establish an explicit `single-letter' characterization of the per-vertex mutual information between the vertex labels and the graph.\n  The explicit expression of the mutual information is intimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08685","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"}