{"paper":{"title":"Navigation in non-uniform density social networks","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Yanqing Hu, Ying Fan, Yong Li, Zengru Di","submitted_at":"2010-10-09T13:18:02Z","abstract_excerpt":"Recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability density distribution of an individual to have a friend at distance $d$ scales as $P(d)\\propto d^{-1}$. Since population density is non-uniform in real social networks, a scale invariant friendship network(SIFN) based on the above empirical law is introduced to capture this phenomenon. We prove the time complexity of navigation in 2-dimensional SIFN is at most $O(\\log^4 n)$. In the real searching experiment, individuals often resort to extra information "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1845","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"}