Spectra of general hypergraphs
For researchers in spectral graph/hypergraph theory, this provides a new representation for general hypergraphs, but the work appears incremental as it extends known spectral properties to a broader class.
The paper proposes a method to reconstruct connectivity hypermatrices for general hypergraphs using tensors and studies their spectral properties, finding similarities with graphs and uniform hypergraphs. This representation aims to advance spectral hypergraph theory.
Here, we show a method to reconstruct connectivity hypermatrices of a general hypergraph (without any self loop or multiple edge) using tensor. We also study the different spectral properties of these hypermatrices and find that these properties are similar for graphs and uniform hypergraphs. The representation of a connectivity hypermatrix that is proposed here can be very useful for the further development in spectral hypergraph theory.