{"paper":{"title":"Universal behavior of optimal paths in weighted networks with general disorder","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Eduardo L\\'opez, H.Eugene Stanley, Shlomo Havlin, Yiping Chen","submitted_at":"2005-08-31T09:17:56Z","abstract_excerpt":"We study the statistics of the optimal path in both random and scale free networks, where weights $w$ are taken from a general distribution $P(w)$. We find that different types of disorder lead to the same universal behavior. Specifically, we find that a single parameter ($S \\equiv AL^{-1/\\nu}$ for $d$-dimensional lattices, and $S\\equiv AN^{-1/3}$ for random networks) determines the distributions of the optimal path length, including both strong and weak disorder regimes. Here $\\nu$ is the percolation connectivity exponent, and $A$ depends on the percolation threshold and $P(w)$. For $P(w)$ un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0508759","kind":"arxiv","version":2},"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"}