On spectral theory of a k-uniform directed hypergraph

Abstract

In this paper, we study a k-uniform directed hypergraph in general form and introduce its associated tensors. We present different spectral properties and show that some of them are generalization of the classical results for undirected hypergraphs. The notation of odd-bipartite directed hypergraph are presented and some spectral properties and characterizations of them comparing with ones in undirected hypergraphs are studied. We also introduce power directed hypergraph and cored directed hypergraph and investigate their spectral properties.