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Multi-way dual Cheeger constants and spectral bounds of graphs

Liu, Shiping

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Authors

Shiping Liu



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.

Citation

Liu, S. (2015). Multi-way dual Cheeger constants and spectral bounds of graphs. Advances in Mathematics, 268, 306-338. https://doi.org/10.1016/j.aim.2014.09.023

Journal Article Type Article
Acceptance Date Sep 29, 2014
Online Publication Date Oct 10, 2014
Publication Date Jan 2, 2015
Deposit Date Aug 14, 2014
Publicly Available Date Oct 13, 2014
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 268
Pages 306-338
DOI https://doi.org/10.1016/j.aim.2014.09.023
Keywords Cheeger constants, Higher-order dual Cheeger inequalities, Spectral clustering, Markov operators, Essential spectrum.

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