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Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians.

Lange, Carsten and Liu, Shiping and Peyerimhoff, Norbert and Post, Olaf (2015) 'Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians.', Calculus of variations and partial differential equations., 54 (4). pp. 4165-4196.


We discuss a Cheeger constant as a mixture of the frustration index and the expansion rate, and prove the related Cheeger inequalities and higher order Cheeger inequalities for graph Laplacians with cyclic signatures, discrete magnetic Laplacians on finite graphs and magnetic Laplacians on closed Riemannian manifolds. In this process, we develop spectral clustering algorithms for partially oriented graphs and multi-way spectral clustering algorithms via metrics in lens spaces and complex projective spaces. As a byproduct, we give a unified viewpoint of Harary’s structural balance theory of signed graphs and the gauge invariance of magnetic potentials.

Item Type:Article
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Publisher statement:This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Date accepted:14 September 2015
Date deposited:01 December 2015
Date of first online publication:05 November 2015
Date first made open access:No date available

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