Hypergraphs and their associated Lie algebras

Abstract

When studying features in networks, communities, and general relations between objects, hypergraphs permit a more complex and accurate description of the underlying data. As hypergraphs admit higher valent relations between vertices, the set of all hypergraphs and their underlying features is infinite, as the number of vertices and the maximum valence of relations present in a hypergraph are both unbounded. In this dissertation, we present a new result which shows that there exists a finite characterization, utilizing the generators of simple Lie algebras, of global features present in a hypergraph. Furthermore, this characterization is implemented as an algorithm to identify specific configurations of relational structures which are present in a given hypergraph.