{"paper":{"title":"Degree-dependent intervertex separation in complex networks","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"J.F.F. Mendes, J.G. Oliveira, S.N. Dorogovtsev","submitted_at":"2004-11-22T17:01:44Z","abstract_excerpt":"We study the mean length $\\ell(k)$ of the shortest paths between a vertex of degree $k$ and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, $\\ell(k) = A\\ln [N/k^{(\\gamma-1)/2}] - C k^{\\gamma-1}/N + ...$ in a wide range of network sizes. Here $N$ is the number of vertices in the network, $\\gamma$ is the degree distribution exponent, and the coefficients $A$ and $C$ depend on a network. We compare this law with a corresponding $\\ell(k)$ dependence obtained for ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0411526","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"}