{"paper":{"title":"Fractional Laplace operator on finite graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mengjie Zhang, Yong Lin, Yunyan Yang","submitted_at":"2024-03-29T05:41:27Z","abstract_excerpt":"Nowadays a great attention has been focused on the discrete fractional Laplace operator as the natural counterpart of the continuous one. In this paper, we discretize the fractional Laplace operator $(-\\Delta)^{s}$ for an arbitrary finite graph and any positive real number $s$. It is shown that $(-\\Delta)^{s}$ can be explicitly represented by eigenvalues and eigenfunctions of the Laplace operator $-\\Delta$. Moreover, we study its important properties, such as $(-\\Delta)^{s}$ converges to $-\\Delta$ as $s$ tends to $1$; while $(-\\Delta)^{s}$ converges to the identity map as $s$ tends to $0$ on a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.19987","kind":"arxiv","version":3},"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/2403.19987/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"}