Spectral theory of Laplace operators on oriented hypergraphs

Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue 1 and the case of duplicate vertices are discussed; two Courant nodal domain theorems are established; new quantities that bound the eigenvalues are introduced. In particular, the C...

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Bibliographic Details
Published inDiscrete mathematics Vol. 344; no. 6; p. 112372
Main Authors Mulas, Raffaella, Zhang, Dong
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2021
Subjects
Cheeger inequality
Chromatic number
Hoffman bound
Laplace operator
Oriented hypergraphs
Spectral theory
Laplace operator
Hoffman bound
Oriented hypergraphs
Spectral theory
Cheeger inequality
Chromatic number
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Summary:Several new spectral properties of the normalized Laplacian defined for oriented hypergraphs are shown. The eigenvalue 1 and the case of duplicate vertices are discussed; two Courant nodal domain theorems are established; new quantities that bound the eigenvalues are introduced. In particular, the Cheeger constant is generalized and it is shown that the classical Cheeger bounds can be generalized for some classes of hypergraphs; it is shown that a geometric quantity used to study zonotopes bounds the largest eigenvalue from below, and that the notion of coloring number can be generalized and used for proving a Hoffman-like bound. Finally, the spectrum of the unnormalized Laplacian for Cartesian products of hypergraphs is discussed.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2021.112372