{"paper":{"title":"The $\\ominus$-metric to compare phylogenetic networks","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Guillaume E. Scholz, Manuel Lafond, Marc Hellmuth","submitted_at":"2026-07-09T09:04:48Z","abstract_excerpt":"We introduce two novel distances for comparing rooted phylogenetic networks based on the $\\ominus$-operator, which removes a vertex while preserving the ancestor relations among the remaining vertices. The distance $d_{\\ominus}$ measures the minimum number of such removals needed to obtain isomorphic networks, whereas $d_{\\ominus}^-$ ignores shortcut arcs and therefore compares the induced ancestry structures. We show that $d_{\\ominus}$ is a metric up to leaf-fixing isomorphism and that $d_{\\ominus}^-$ is a metric up to shortcut-free isomorphism. Moreover, both distances extend the Robinson--F"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08259","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08259/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}