{"paper":{"title":"Consistency of Spectral Seriation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaron Smith, Amine Natik","submitted_at":"2021-12-08T16:53:45Z","abstract_excerpt":"Consider a random graph $G$ of size $N$ constructed according to a \\textit{graphon} $w \\, : \\, [0,1]^{2} \\mapsto [0,1]$ as follows. First embed $N$ vertices $V = \\{v_1, v_2, \\ldots, v_N\\}$ into the interval $[0,1]$, then for each $i < j$ add an edge between $v_{i}, v_{j}$ with probability $w(v_{i}, v_{j})$. Given only the adjacency matrix of the graph, we might expect to be able to approximately reconstruct the permutation $\\sigma$ for which $v_{\\sigma(1)} < \\ldots < v_{\\sigma(N)}$ if $w$ satisfies the following \\textit{linear embedding} property introduced in [Janssen 2019]: for each $x$, $w("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04408","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/2112.04408/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"}