Intersection Graphs of Oriented Hypergraphs and Their Matrices

Abstract

For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are investigated including the incidence dual, the intersection graph (line graph), and the 2-section. A connection is then made between oriented hypergraphs and balanced incomplete block designs.