{"paper":{"title":"Counting Triangles of Graphs via Randomized Trace Estimation with Incomplete Matrix-Vector Products","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Lior Horesh, Shashanka Ubaru, Soumyadip Ghosh, Tomasz Nowicki, Vasileios Kalantzis, Yingdong Lu","submitted_at":"2026-06-21T18:31:29Z","abstract_excerpt":"Counting triangles in graphs is a fundamental operation in network analysis, underpinning metrics such as clustering coefficients and serving as a signal for community detection, link prediction, and anomaly detection. The standard approach computes the trace of the cube of the adjacency matrix, but explicitly forming $\\mathbf{A}^3$ is infeasible for large graphs. Hutchinson randomized trace estimator offers an efficient alternative by approximating the trace through stochastic averaging of quadratic forms, requiring only matrix vector products with $\\mathbf{A}$. However, in distributed and he"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22629","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}