{"paper":{"title":"The maximum average connectivity among all orientations of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lucas Mol, Ortrud R. Oellermann, Peter Dankelmann, Rocio M. Casablanca, Wayne Goddard","submitted_at":"2019-07-16T19:08:20Z","abstract_excerpt":"For distinct vertices $u$ and $v$ in a graph $G$, the {\\em connectivity} between $u$ and $v$, denoted $\\kappa_G(u,v)$, is the maximum number of internally disjoint $u$--$v$ paths in $G$. The {\\em average connectivity} of $G$, denoted $\\overline{\\kappa}(G),$ is the average of $\\kappa_G(u,v)$ taken over all unordered pairs of distinct vertices $u,v$ of $G$. Analogously, for a directed graph $D$, the {\\em connectivity} from $u$ to $v$, denoted $\\kappa_D(u,v)$, is the maximum number of internally disjoint directed $u$--$v$ paths in $D$. The {\\em average connectivity} of $D$, denoted $\\overline{\\ka"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07219","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"}