{"paper":{"title":"Structural Transitions in Dense Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"P. L. Krapivsky, R. Lambiotte, S. Redner, U. Bhat","submitted_at":"2016-07-13T18:16:40Z","abstract_excerpt":"We introduce an evolving network model in which a new node attaches to a randomly selected target node and also to each of its neighbors with probability $p$. The resulting network is sparse for $p<\\frac{1}{2}$ and dense (average degree increasing with number of nodes $N$) for $p\\geq \\frac{1}{2}$. In the dense regime, individual networks realizations built by this copying mechanism are disparate and not self-averaging. Further, there is an infinite sequence of structural anomalies at $p=\\frac{2}{3}$, $\\frac{3}{4}$, $\\frac{4}{5}$, etc., where the dependences on $N$ of the number of triangles (3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03850","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":""},"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"}