Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians

被引：23

作者：

Lange, Carsten ^{[1
,2
]}

Liu, Shiping ^{[3
]}

Peyerimhoff, Norbert ^{[3
]}

Post, Olaf ^{[4
]}

机构：

[1] Free Univ Berlin, Fachbereich Math & Informat, D-14195 Berlin, Germany

[2] Tech Univ Munich, Zentrum Math, D-85748 Garching, Germany

[3] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

[4] Univ Trier, Fachbereich Math 4, D-54286 Trier, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 54卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

SCHRODINGER-OPERATORS; ISOPERIMETRIC INEQUALITY; MAX CUT; EIGENVALUE; GRAPHS; SPECTRUM; BIPARTITE;

D O I：

10.1007/s00526-015-0935-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：4165 / 4196

页数：32

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