Pareto H-eigenvalues of nonnegative tensors and uniform hypergraphs

Abstract

The Pareto H-eigenvalues of nonnegative tensors and (adjacency tensors of) uniform hypergraphs are studied. Particularly, it is shown that the Pareto H-eigenvalues of a nonnegative tensor are just the spectral radii of its weakly irreducible principal subtensors, and those hypergraphs that minimize or maximize the second largest Pareto H-eigenvalue over several well-known classes of uniform hypergraphs are determined.