{"paper":{"title":"Spectral density of the non-backtracking operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"cond-mat.dis-nn","authors_text":"Alaa Saade, Florent Krzakala, Lenka Zdeborov\\'a","submitted_at":"2014-04-30T16:36:22Z","abstract_excerpt":"The non-backtracking operator was recently shown to provide a significant improvement when used for spectral clustering of sparse networks. In this paper we analyze its spectral density on large random sparse graphs using a mapping to the correlation functions of a certain interacting quantum disordered system on the graph. On sparse, tree-like graphs, this can be solved efficiently by the cavity method and a belief propagation algorithm. We show that there exists a paramagnetic phase, leading to zero spectral density, that is stable outside a circle of radius $\\sqrt{\\rho}$, where $\\rho$ is th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7787","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"}