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In this paper we generalize and improve the multiscale organization of graphsby introducing a new measure that quantifies the "closeness" between two nodes.The calculation of the measure is linear in the number of edges in the graphand involves just a small number of relaxation sweeps. A similar notion ofdistance is then calculated and used at each coarser level. We demonstrate theuse of this measure in multiscale methods for several important combinatorialoptimization problems and discuss the multiscale graph organization.

Relaxation-Based Coarsening and Multiscale Graph Organization