{"paper":{"title":"Non-Backtracking Spectrum of Degree-Corrected Stochastic Block Models","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":"2016-09-08T16:33:39Z","abstract_excerpt":"Motivated by community detection, we characterise the spectrum of the non-backtracking matrix $B$ in the Degree-Corrected Stochastic Block Model.\n  Specifically, we consider a random graph on $n$ vertices partitioned into two equal-sized clusters. The vertices have i.i.d. weights $\\{ \\phi_u \\}_{u=1}^n$ with second moment $\\Phi^{(2)}$. The intra-cluster connection probability for vertices $u$ and $v$ is $\\frac{\\phi_u \\phi_v}{n}a$ and the inter-cluster connection probability is $\\frac{\\phi_u \\phi_v}{n}b$.\n  We show that with high probability, the following holds: The leading eigenvalue of the no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02487","kind":"arxiv","version":2},"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"}