{"paper":{"title":"Large Communities in a scale-free network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Caio Alves, Remy Sanchis, Rodrigo Ribeiro","submitted_at":"2015-09-15T17:18:55Z","abstract_excerpt":"We prove the existence of a large complete subgraph w.h.p. in a preferential attachment random graph process with an edge-step. That is, we prove that the random graph $G_{t}$ produced by the so-called GLP model at time $t$ contains a complete subgraph of order $t^\\alpha$, where $\\alpha = (1-\\varepsilon)\\frac{1-p}{2-p}$, $\\varepsilon$ is any number such that $0<\\varepsilon<1$, and $0<p<1$ is a parameter of the model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04650","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":""},"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"}