{"paper":{"title":"Scale-Free Networks Emerging from Weighted Random Graphs","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"H. Eugene Stanley, Lidia A. Braunstein, Sameet Sreenivasan, Sergey V. Buldyrev, Shlomo Havlin, Tomer Kalisky","submitted_at":"2005-03-24T12:51:17Z","abstract_excerpt":"We study Erd\\\"{o}s-R\\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters) into a single node. We show that this network is scale-free, i.e., the degree distribution is $P(k)\\sim k^{-\\lambda}$ with $\\lambda=2.5$. Our results imply that the minimum spanning tree (MST) in random graphs is composed of percolation clusters, which are interconnected by a set of links that create a scale-free tree with $\\lambda=2.5$. We show that optimizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0503598","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"}