{"paper":{"title":"Stability of the Centrality of Unions of Networks on the Same Vertex Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","math.CO"],"primary_cat":"nlin.AO","authors_text":"Chuan Wen, Henrik Jeldtoft Jensen, Loe","submitted_at":"2013-09-25T07:38:33Z","abstract_excerpt":"Let $G^1(V,E_1)$ and $G^2(V,E_2)$ be two networks on the same vertex set $V$ and consider the union of edges $G(V, E_1 \\cup E_2)$. This paper studies the stability of the Degree, Betweenness and Eigenvector Centrality of the resultant network, $G(V, E_1 \\cup E_2)$. Specifically assume $v^1_{max}$ and $v^c_{max}$ are the highest centrality vertices of $G^1(V,E_1)$ and $G(V, E_1 \\cup E_2)$ respectively, we want to find $Pr(v^1_{max} = v^c_{max})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6629","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"}