{"paper":{"title":"On the roots of the node reliability polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.CO","authors_text":"Jason Brown, Lucas Mol","submitted_at":"2016-07-28T15:12:35Z","abstract_excerpt":"Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce; it is the analogous node measure of robustness to the well studied \\textit{all-terminal reliability}, where the nodes are perfectly reliable but the edges fail randomly. In sharp contrast to what is known about the roots of the all-terminal reliability polynomial, we show that the node reliability polyn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08496","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"}