{"paper":{"title":"Persistence of hubs in growing random networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sayan Banerjee, Shankar Bhamidi","submitted_at":"2020-04-28T19:33:35Z","abstract_excerpt":"We consider models of evolving networks $\\{\\mathcal{G}_n:n\\geq 0\\}$ modulated by two parameters: an attachment function $f:\\mathbb{N}_0\\to\\mathbb{R}_+$ and a (possibly random) attachment sequence $\\{m_i:i\\geq 1\\}$. Starting with a single vertex, at each discrete step $i\\geq 1$ a new vertex $v_i$ enters the system with $m_i\\geq 1$ edges which it sequentially connects to a pre-existing vertex $v\\in \\mathcal{G}_{i-1}$ with probability proportional to $f(\\operatorname{degree}(v))$. We consider the problem of emergence of persistent hubs: existence of a finite (a.s.) time $n^*$ such that for all $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.13785","kind":"arxiv","version":2},"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/2004.13785/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"}