{"paper":{"title":"Average path length in random networks","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Agata Fronczak, Janusz A. Holyst, Piotr Fronczak","submitted_at":"2002-12-10T19:51:04Z","abstract_excerpt":"Analytic solution for the average path length in a large class of random graphs is found. We apply the approach to classical random graphs of Erd\\\"{o}s and R\\'{e}nyi (ER) and to scale-free networks of Barab\\'{a}si and Albert (BA). In both cases our results confirm previous observations: small world behavior in classical random graphs $l_{ER} \\sim \\ln N$ and ultra small world effect characterizing scale-free BA networks $l_{BA} \\sim \\ln N/\\ln\\ln N$. In the case of scale-free random graphs with power law degree distributions we observed the saturation of the average path length in the limit of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0212230","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"}