{"paper":{"title":"Spectral methods for testing cluster structure of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jonathan Tidor, Sandeep Silwal","submitted_at":"2018-12-30T16:08:13Z","abstract_excerpt":"In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \\phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has conductance at least $\\phi$. We present an algorithm that accepts all graphs that are $(2, \\phi)$-clusterable with probability at least $\\frac{2}3$ and rejects all graphs that are $\\epsilon$-far from $(2, \\phi^*)$-clusterable for $\\phi^* \\le \\mu \\phi^2 \\epsilon^2$ with probability at least $\\frac{2}3$ where $\\mu > 0$ is a parameter that affects the query compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11564","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"}