{"paper":{"title":"SBM With Multiple Samples: Improved Spectral Recovery","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Peter Chin, Sie Hendrata Dharmawan","submitted_at":"2026-06-23T04:49:17Z","abstract_excerpt":"We study community detection in the two-block stochastic block model under the setting where multiple independent graph samples drawn from the same distribution are available. Building on a recently simplified spectral algorithm that preserves the independence of adjacency matrix entries throughout, we show that averaging $m$ independent samples before applying spectral partitioning reduces the error bound $\\gamma$ exponentially in $m$: specifically, one can find a $\\gamma$-correct partition with probability $1 - o(1)$ whenever $\\frac{(a-b)^2}{a+b} \\geq \\frac{C}{m} \\log \\frac{2}{\\gamma}$, impr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24141","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.24141/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}