Computing Diffusion State Distance using Green's Function and Heat Kernel on Graphs [article]

Edward Boehnlein, Peter Chin, Amit Sinha, Linyuan Lu
2014 arXiv   pre-print
The diffusion state distance (DSD) was introduced by Cao-Zhang-Park-Daniels-Crovella-Cowen-Hescott [ 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 [ J.
more » ... atorial Theory (A), 2000]. Based on that, we computed the DSD L_q-distance for Paths, Cycles, Hypercubes, as well as random graphs G(n,p) and G(w_1,..., w_n). We also examined the DSD distances of two biological networks.
arXiv:1410.3168v1 fatcat:vdh5u637wvgvtdtezkwtwlf64a