Abstract
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of either +1 or −1. This generalizes signed graphs to a hypergraph setting and simultaneously provides a natural definition for a signed adjacency which is used to define the adjacency and Laplacian matrices. Many properties of these matrices are known, but there are no nontrivial families of oriented hypergraphs with their spectrum determined. In this paper we define and study hypergraph families that are analogous to cycles and paths in graphs and signed graphs. The adjacency and Laplacian eigenvalues for some of these families is determined.
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