H+-eigenvalues of Laplacian and signless Laplacian tensors

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.