Short Introduction to SuperHyperGraph Theory with some applications

Abstract

A finite hypergraph extends an ordinary graph by permitting each hyperedge to connect an arbitrary nonempty subset
of vertices, thereby encoding genuinely multiway interactions. Building on this idea, a finite SuperHyperGraph is formed by iterating the powerset construction, so that set-valued objects created at one level can act as vertices (and hence as potential edge endpoints) at the next. This provides a principled framework for representing hierarchical, nested, and multilayer relational structures. In this paper, we introduce SuperHyperGraphs and several related concepts, illustrating them with concrete examples.