Multi-way dual Cheeger constants and spectral bounds of graphs

Shiping Liu

doi:10.1016/j.aim.2014.09.023

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arXiv · 1401.3147

Multi-way dual Cheeger constants and spectral bounds of graphs

Shiping Liu

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Abstract

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.

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Shiping Liu. 2014-08-15. Multi-way dual Cheeger constants and spectral bounds of graphs. https://doi.org/10.1016/j.aim.2014.09.023

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