{"paper":{"title":"Counting k-Hop Paths in the Random Connection Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander P. Kartun-Giles, Sunwoo Kim","submitted_at":"2017-04-21T05:01:10Z","abstract_excerpt":"We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than determinist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06400","kind":"arxiv","version":3},"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"}