{"paper":{"title":"Estimating graph parameters with random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Anna Ben-Hamou, Roberto I. Oliveira, Yuval Peres","submitted_at":"2017-09-04T08:58:43Z","abstract_excerpt":"An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up to a bounded factor in $O\\left(t_{\\mathrm{rel}}^{3/4}\\sqrt{m/d}\\right)$ steps, where $t_{\\mathrm{rel}}$ is the relaxation time of the lazy random walk on $G$ and $d$ is the minimum degree in $G$. Alternatively, $m$ can be estimated in $O\\left(t_{\\mathrm{unif}} +t_{\\mathrm{rel}}^{5/6}\\sqrt{n}\\right)$, where $n$ is the number of vertices and $t_{\\mathrm{unif}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00869","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"}