{"paper":{"title":"Fractal Boundaries of Complex Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.MP","physics.data-an","physics.soc-ph"],"primary_cat":"math-ph","authors_text":"H. Eugene Stanley, Jia Shao, Maksim Kitsak, Reuven Cohen, Sergey V. Buldyrev, Shlomo Havlin","submitted_at":"2008-04-11T21:18:53Z","abstract_excerpt":"We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We find that for both Erd\\\"{o}s-R\\'{e}nyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes {\\it B} follows a power-law probability density function which scales as $B^{-2}$. The clusters formed by the boundary nodes are fractals with a fractal dimension $d_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.1968","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"}