{"paper":{"title":"An Impossibility Result for Reconstruction in a Degree-Corrected Planted-Partition Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SI","stat.ML"],"primary_cat":"math.PR","authors_text":"Laurent Massouli\\'e, Lennart Gulikers, Marc Lelarge","submitted_at":"2015-11-02T15:30:40Z","abstract_excerpt":"We consider the Degree-Corrected Stochastic Block Model (DC-SBM): a random graph on $n$ nodes, having i.i.d. weights $(\\phi_u)_{u=1}^n$ (possibly heavy-tailed), partitioned into $q \\geq 2$ asymptotically equal-sized clusters. The model parameters are two constants $a,b > 0$ and the finite second moment of the weights $\\Phi^{(2)}$. Vertices $u$ and $v$ are connected by an edge with probability $\\frac{\\phi_u \\phi_v}{n}a$ when they are in the same class and with probability $\\frac{\\phi_u \\phi_v}{n}b$ otherwise.\n  We prove that it is information-theoretically impossible to estimate the clusters in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00546","kind":"arxiv","version":3},"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"}