Abstract
A hypergraph is a generalization of a graph since, in a graph an edge relates only a pair of points, but the edges of a hypergraph known as hyperedges can relate groups of more than two points. The representation of complex systems as graphs is appropriate for the study of certain problems. We give several examples of social, biological, ecological and technological systems where the use of graphs gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems.
Highlights
The calculus of relations has been an important component of the development of logic and algebra since the middle of the nineteenth century
The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges
Using Lemmas 1 and 2, it follows that the edges of a competition hypergraph of an acyclic digraph D correspond to the columns of a strictly lower triangular adjacency matrix M of D
Summary
A hypergraph is a generalization of a graph since, in a graph an edge relates only a pair of points, but the edges of a hypergraph known as hyperedges can relate groups of more than two points. The representation of complex systems as graphs is appropriate for the study of certain problems. We give several examples of social, biological, ecological and technological systems where the use of graphs gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems
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