{"paper":{"title":"Distances in random graphs with finite mean and infinite variance degrees","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Dmitri Znamenski, Gerard Hooghiemstra, Remco van der Hofstad","submitted_at":"2005-02-28T16:51:58Z","abstract_excerpt":"In this paper we study random graphs with independent and identically distributed degrees of which the tail of the distribution function is regularly varying with exponent $\\tau\\in (2,3)$.\n  The number of edges between two arbitrary nodes, also called the graph distance or hopcount, in a graph with $N$ nodes is investigated when $N\\to \\infty$. When $\\tau\\in (2,3)$, this graph distance grows like $2\\frac{\\log\\log N}{|\\log(\\tau-2)|}$. In different papers, the cases $\\tau>3$ and $\\tau\\in (1,2)$ have been studied. We also study the fluctuations around these asymptotic means, and describe their dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502581","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"}