H-eigenvalues of Laplacian and Signless Laplacian Tensors
نویسنده
چکیده
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.
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