{"paper":{"title":"How beta-skeletons lose their edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andrew Adamatzky","submitted_at":"2013-12-27T22:30:13Z","abstract_excerpt":"A {\\beta}-skeleton is a proximity graphs with node neighbourhood defined by continuous-valued parameter {\\beta}. Two nodes in a {\\beta}-skeleton are connected by an edge if their lune-based neighbourhood contains no other nodes. With increase of {\\beta} some edges a skeleton are disappear. We study how a number of edges in {\\beta}-skeleton depends on {\\beta}. We speculate how this dependence can be used to discriminate between random and non-random planar sets. We also analyse stability of {\\beta}-skeletons and their sensitivity to perturbations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7363","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"}