On the spectrum of directed uniform and non-uniform hypergraphs
This work advances spectral hypergraph theory by providing a framework for directed hypergraphs, benefiting researchers in algebraic graph theory and network analysis.
The authors propose a tensor-based representation for directed uniform and non-uniform hypergraphs and extend spectral properties from undirected to directed uniform hypergraphs, introducing weak* irreducible hypermatrices for connectivity analysis.
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.