{"paper":{"title":"Percolation in networks composed of connectivity and dependency links","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":"Amir Bashan, Roni Parshani, Shlomo Havlin","submitted_at":"2011-01-11T07:48:57Z","abstract_excerpt":"Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second order transition found in classical networks. We analytically analyze the effect of different distributions of dependencies links on the robustness of networks. For a random Erd$\\ddot{o}$s-R$\\acute{e}$nyi (ER) network with average degree $k$ that is divided into dependency clusters of size $s$, the fraction of nodes that belong to the giant component, $P_\\infty$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2057","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"}