A Cheeger Inequality for Size-Specific Conductance

03/20/2023

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by   Yufan Huang, et al.

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The μ-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 μ fraction of the whole graph. Using μ-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 μ-conductance and show the optimum of this program has a two-sided Cheeger inequality with μ-conductance.