Spectral Properties of Oriented Hypergraphs

Abstract

An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an oriented hypergraph which depend on structural parameters of the oriented hypergraph are found. An oriented hypergraph and its incidence dual are shown to have the same nonzero Laplacian eigenvalues. A family of oriented hypergraphs with uniformally labeled incidences is also studied. This family provides a hypergraphic generalization of the signless Laplacian of a graph and also suggests a natural way to define the adjacency and Laplacian matrices of a hypergraph. Some results presented generalize both graph and signed graph results to a hypergraphic setting.

For the published version of the article see http://repository.uwyo.edu/ela/vol27/iss1/24/

References in corpus (3)

• Spectral Properties of Complex Unit Gain Graphs
• An Oriented Hypergraphic Approach to Algebraic Graph Theory
• An analytic theory of extremal hypergraph problems

Cited by in corpus (15)

• Spectral Theory of Laplace Operators on Oriented Hypergraphs
• Incidence Hypergraphs: Injectivity, Uniformity, and Matrix-tree Theorems
• The Signless Laplacian Matrix of Hypergraphs
• Normalized Laplace Operators for Hypergraphs with Real Coefficients
• Coloring the normalized Laplacian for oriented hypergraphs
• Sharp bounds for the largest eigenvalue
• Geometry and symmetry in biochemical reaction systems
• Spectra of hyperstars on public transportation networks
• Intersection Graphs of Oriented Hypergraphs and Their Matrices
• Incidence Hypergraphs: Box Products & the Laplacian
• A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs
• Spectral classes of hypergraphs
• The Determinant of $\{\pm 1\}$-Matrices and Oriented Hypergraphs
• Spectral theory of weighted hypergraphs via tensors
• Interlacing Results for Hypergraphs