Hypergraphs: an introduction and review

TL;DR

This paper provides an overview of hypergraphs, comparing various definitions, discussing mathematical properties, and exploring visualization techniques, serving as a comprehensive introduction and review of their theoretical and practical aspects.

Contribution

It offers a comparative analysis of hypergraph definitions and presents unpublished visualization methods, filling gaps in the literature and aiding understanding of hypergraph applications.

Findings

Different hypergraph definitions are compared.

Unpublished visualization techniques are introduced.

The review highlights key mathematical and practical aspects of hypergraphs.

Abstract

Hypergraphs were introduced in 1973 by Berg\'e. This review aims at giving some hints on the main results that we can find in the literature, both on the mathematical side and on their practical usage. Particularly, different definitions of hypergraphs are compared, some unpublished work on the visualisation of large hypergraphs done by the author. This review does not pretend to be exhaustive.