  Here, we suggest a method to represent general directed uniform and
non-uniform hypergraphs by different connectivity tensors. We show many results
on spectral properties of undirected hypergraphs also hold for general directed
uniform hypergraphs. Our representation of a connectivity tensor will be very
useful for the further development in spectral theory of directed hypergraphs.
At the end, we have also introduced the concept of weak* irreducible
hypermatrix to better explain connectivity of a directed hypergraph.
