Intersection Graphs of Oriented Hypergraphs and Their Matrices

TL;DR

This paper explores the matrices associated with oriented hypergraphs, such as adjacency and Laplacian matrices, and investigates related structures like intersection graphs and their connection to block designs.

Contribution

It introduces a framework for defining and analyzing matrices of oriented hypergraphs and links these structures to balanced incomplete block designs.

Findings

Defined adjacency and Laplacian matrices for oriented hypergraphs

Analyzed the intersection graph and 2-section of hypergraphs

Established connections between hypergraph orientations and block designs

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.