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arXiv · 2303.11452

A Cheeger Inequality for Size-Specific Conductance

Yufan Huang·David F. Gleich
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Abstract

The $\mu$-conductance measure proposed by Lov\'asz 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 the network structures in new ways. In this manuscript we study a modified spectral cut for $\mu$-conductance that is a natural relaxation of the integer program of $\mu$-conductance and show that the optimum of this program has a two-sided Cheeger inequality with $\mu$-conductance.

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Yufan Huang, David F. Gleich. 2023-03-20. A Cheeger Inequality for Size-Specific Conductance. https://arxiv.org/abs/2303.11452

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