{"paper":{"title":"On the Degree Distribution of P\\'{o}lya Urn Graph Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.soc-ph"],"primary_cat":"math.PR","authors_text":"Ali Jadbabaie, Eric Eaton, Haitham Bou Ammar, Rasul Tutunov","submitted_at":"2014-10-30T19:42:59Z","abstract_excerpt":"This paper presents a tighter bound on the degree distribution of arbitrary P\\'{o}lya urn graph processes, proving that the proportion of vertices with degree $d$ obeys a power-law distribution $P(d) \\propto d^{-\\gamma}$ for $d \\leq n^{\\frac{1}{6}-\\epsilon}$ for any $\\epsilon > 0$, where $n$ represents the number of vertices in the network. Previous work by Bollob\\'{a}s et al. formalized the well-known preferential attachment model of Barab\\'{a}si and Albert, and showed that the power-law distribution held for $d \\leq n^{\\frac{1}{15}}$ with $\\gamma = 3$. Our revised bound represents a signific"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8515","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"}