Spectra of complex unit hypergraphs
Raffaella Mulas and Nathan Reff
Abstract
A complex unit hypergraph is a hypergraph where each vertex-edge incidence is given a complex unit label. We define the adjacency, incidence, Kirchoff Laplacian and normalized Laplacian of a complex unit hypergraph and study each of them. Eigenvalue bounds for the adjacency, Kirchoff Laplacian and normalized Laplacian are also found. Complex unit hypergraphs naturally generalize several hypergraphic structures such as oriented hypergraphs, where vertex-edge incidences are labelled as either +1 or -1, as well as ordinary hypergraphs. Complex unit hypergraphs also generalize their graphic analogues, which are complex unit gain graphs, signed graphs, and ordinary graphs.
Spectra of Complex Unit Hypergraphs | The Art of Discrete and Applied Mathematics
The Art of Discrete and Applied Mathematics (ADAM) is a modern, dynamic, platinum open access, electronic journal that will publish high-quality articles of arbitrary length in contemporary discrete and applied mathematics in which neither the authors nor the readers incur any costs.
Authors Raffaella Mulas Max Planck Institute for Mathematics in the Sciences