Study on Hypergraphs and Directed Hypergraphs

Exploring the Applications of Hypergraphs and Directed Hypergraphs in Various Fields

Abstract

A graph is often thought of as an abstract structure that represents the pairwise connections between collections of objects known as vertices. Two vertices may be linked by an edge or can exist independently of one another. Allowing an edge to link an arbitrary number of vertices is one method to broaden this notion. Hyperedges are subsets of the vertex set, and they are referred to as such. A hypergraph is made up of a set of vertices and a family of hyperedges. Hypergraphs are more abstract than graphs, having less structure. Hypergraphs, rather than graphs, are better suited as a modelling paradigm in certain situations. Hypergraphs are used to simulate tram lines in [Karbstein, 2012]) and railway vehicle coupling in [Borndörfer et al., 2012] in the area of transportation planning. See [Eiter and Gottlob, 1995] for examples of hypergraphs in the fields of logic and artificial intelligence. In addition, both directed and undirected hypergraphs are effectively employed in the area of biological networks analysis for a brief review, see [Klamt et al., 2009]. Protein interactions, for example, often include more than one protein, therefore hyperedges rather than edges may be utilised to simulate them more correctly.