{"paper":{"title":"A parameterized family of balance indices for phylogenetic networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","q-bio.PE"],"primary_cat":"math.CO","authors_text":"Fran\\c{c}ois Bienvenu, Hadrien Maffioli, Jean-Jil Duchamps","submitted_at":"2026-06-23T13:29:58Z","abstract_excerpt":"We introduce a new family of balance indices for phylogenetic networks: the $H_\\alpha$ indices, where $\\alpha$ is a positive real number. This family includes the $B_2$ index as a special case ($\\alpha = 1$) and provides a natural extension of the Sackin index to phylogenetic networks. We show that the $H_\\alpha$ indices share many structural properties with the $B_2$ index, most notably a \"grafting property\" that makes it possible to express the $H_\\alpha$ index of a network in terms of the $H_\\alpha$ indices of its biconnected components. These properties allow us to identify networks that m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24562","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/2606.24562/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"}