{"paper":{"title":"Computing Diffusion State Distance using Green's Function and Heat Kernel on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amit Sinha, Edward Boehnlein, Linyuan Lu, Peter Chin","submitted_at":"2014-10-13T00:20:40Z","abstract_excerpt":"The diffusion state distance (DSD) was introduced by Cao-Zhang-Park-Daniels-Crovella-Cowen-Hescott [{\\em PLoS ONE, 2013}] to capture functional similarity in protein-protein interaction networks. They proved the convergence of DSD for non-bipartite graphs. In this paper, we extend the DSD to bipartite graphs using lazy-random walks and consider the general $L_q$-version of DSD. We discovered the connection between the DSD $L_q$-distance and Green's function, which was studied by Chung and Yau [{\\em J. Combinatorial Theory (A), 2000}]. Based on that, we computed the DSD $L_q$-distance for Paths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3168","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"}