Communications in Mathematical Sciences· 2014Q1
H<sup>+</sup>-eigenvalues of Laplacian and signless Laplacian tensors
- 183citations
- Q1SCImago
- 2014year
Short summary
This paper defines Laplacian and signless Laplacian tensors for uniform hypergraphs and studies their H+-eigenvalues (nonnegative eigenvectors) and H++-eigenvalues (positive eigenvectors). It shows these tensors have at most one H++-eigenvalue and identifies properties of their largest and smallest H+-eigenvalues.
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Key points
- Introduced definitions for Laplacian and signless Laplacian tensors of uniform hypergraphs.
- Studied H+-eigenvalues (nonnegative eigenvectors) and H++-eigenvalues (positive eigenvectors).
- Proved that Laplacian and signless Laplacian tensors have at most one H++-eigenvalue.
- Identified largest and smallest H+-eigenvalues and established their maximum/minimum properties.
- Defined analytic connectivity for uniform hypergraphs and discussed its application to edge connectivity.
AI-generated from the title and abstract; the full text is not read.
Abstract
We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H + -eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H ++ -eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H ++ -eigenvalue, but has several other H + -eigenvalues. We identify their largest and smallest H + -eigenvalues, and establish some maximum and minimum properties of these H + -eigenvalues. We then define analytic connectivity of a uniform hypergraph and discuss its application in edge connectivity.
The authors' abstract, as published at the source. Communications in Mathematical Sciences, 2014 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics