{"paper":{"title":"Creating and controlling overlap in two-layer networks. Application to a mean-field SIS epidemic model with awareness dissemination","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"physics.soc-ph","authors_text":"David Juher, Joan Salda\\~na","submitted_at":"2015-04-08T16:44:40Z","abstract_excerpt":"We study the properties of the potential overlap between two networks $A,B$ sharing the same set of $N$ nodes (a two-layer network) whose respective degree distributions $p_A(k), p_B(k)$ are given. Defining the overlap coefficient $\\alpha$ as the Jaccard index, we derive upper bounds for the minimum and maximum overlap coefficient in terms of $p_A(k)$, $p_B(k)$ and $N$. We also present an algorithm based on cross-rewiring of links to obtain a two-layer network with any prescribed $\\alpha$ inside the permitted range. Finally, to illustrate the importance of the overlap for the dynamics of inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02031","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"}