{"paper":{"title":"An Efficient Algorithm for Unweighted Spectral Graph Sparsification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christopher Melgaard, David G. Anderson, Ming Gu","submitted_at":"2014-10-16T01:53:01Z","abstract_excerpt":"Spectral graph sparsification has emerged as a powerful tool in the analysis of large-scale networks by reducing the overall number of edges, while maintaining a comparable graph Laplacian matrix. In this paper, we present an efficient algorithm for the construction of a new type of spectral sparsifier, the unweighted spectral sparsifier. Given a general undirected and unweighted graph $G = (V, E)$ and an integer $\\ell < |E|$ (the number of edges in $E$), we compute an unweighted graph $H = (V, F)$ with $F \\subset E$ and $|F| = \\ell$ such that for every $x \\in \\mathbb{R}^{V}$ \\[ {\\displaystyle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4273","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"}