Tropical spectral theory of tensors

We introduce and study tropical eigenpairs of tensors, a generalization of the tropical spectral theory of matrices. We show the existence and uniqueness of an eigenvalue. We associate with a tensor a directed hypergraph and define a new type of cycle on such a hypergraph, which we call an H-cycle. The eigenvalue of a tensor turns out to be equal to the minimal normalized weighted length of H-cycles of the associated hypergraph. We show that the eigenvalue can be computed efficiently via a linear program.