{"paper":{"title":"General Clique Percolation in Network Evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jingfang Fan, Xiaosong Chen","submitted_at":"2013-09-18T04:50:19Z","abstract_excerpt":"We introduce a general $(k,l)$ clique community, which consists of adjacent $k$-cliques sharing at least $l$ vertices with $k-1 \\ge l \\ge 1$. The emergence of a giant $(k,l)$ clique community indicates a $(k,l)$ clique percolation, which is studied by the largest size gap $\\Delta$ of the largest clique community during network evolution and the corresponding evolution step $T_c$. For a clique percolation, the averages of $\\Delta$ and $T_c$ and the root-mean-squares of their fluctuations have power law finite-size effects whose exponents are related to the critical exponents. The fluctuation di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4535","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"}