{"paper":{"title":"Towards $k$-connectivity of the random graph induced by a pairwise key predistribution scheme with unreliable links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.IT","math.CO","math.IT","math.PR"],"primary_cat":"cs.DM","authors_text":"Faruk Yavuz, Jun Zhao, Osman Ya\\u{g}an, Virgil Gligor","submitted_at":"2014-04-19T17:27:58Z","abstract_excerpt":"We study the secure and reliable connectivity of wireless sensor networks. Security is assumed to be ensured by the random pairwise key predistribution scheme of Chan, Perrig, and Song, and unreliable wireless links are represented by independent on/off channels. Modeling the network by an intersection of a random $K$-out graph and an Erd\\H{o}s-R\\'enyi graph, we present scaling conditions (on the number of nodes, the scheme parameter $K$, and the probability of a wireless channel being on) such that the resulting graph contains no nodes with degree less than $k$ with high probability, when the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5193","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"}