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A Cheeger Inequality for Size-Specific Conductance (2303.11452v1)
Published 20 Mar 2023 in cs.DM and cs.SI
Abstract: The $\mu$-conductance measure proposed by Lovasz and Simonovits is a size-specific conductance score that identifies the set with smallest conductance while disregarding those sets with volume smaller than a $\mu$ fraction of the whole graph. Using $\mu$-conductance enables us to study in new ways. In this manuscript we propose a modified spectral cut that is a natural relaxation of the integer program of $\mu$-conductance and show the optimum of this program has a two-sided Cheeger inequality with $\mu$-conductance.