{"paper":{"title":"Clique percolation in random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Bing-Hong Wang, Ming Li, Youjin Deng","submitted_at":"2015-08-08T09:58:07Z","abstract_excerpt":"As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l<k$ vertices. In this paper, we develop a theoretical approach to study clique percolation in Erd\\H{o}s-R\\'{e}nyi graphs, which gives not only the exact solutions of the critical point, but also the corresponding order parameter. Based on this, we prove theoretically that the fraction $\\psi$ of cliques in the giant clique cluster always makes a continuous phase transition as the classical percolation. However,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01878","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"}