{"paper":{"title":"Asymptotic Traffic Flow in a Hyperbolic Network: Non-uniform Traffic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.NI","math-ph","math.MG","math.MP"],"primary_cat":"math.GR","authors_text":"Gabriel H. Tucci, Yuliy Baryshnikov","submitted_at":"2010-10-16T02:06:48Z","abstract_excerpt":"In this work we study the asymptotic traffic flow in Gromov's hyperbolic graphs when the traffic decays exponentially with the distance. We prove that under general conditions, there exists a phase transition between local and global traffic. More specifically, assume that the traffic rate between two nodes $u$ and $v$ is given by $R(u,v)=\\beta^{-d(u,v)}$ where $d(u,v)$ is the distance between the nodes. Then there exists a constant $\\beta_c$ that depends on the geometry of the network such that if $1<\\beta<\\beta_c$ the traffic is global and there is a small set of highly congested nodes calle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3305","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"}