%0 Journal Article
%T H$^+$-Eigenvalues of Laplacian and Signless Laplacian Tensors
%A Liqun Qi
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1303.2186v2