Conceptual HyperGraph and Conceptual SuperHyperGraph

Abstract. A finite hypergraph generalizes an ordinary graph by permitting a hyperedge to connect any
nonempty subset of vertices, thereby capturing multiway interactions. Extending this idea, a finite Super
HyperGraph is obtained by iterating the powerset operation, producing nested families of vertex and edge
sets that model multi-layer relational structure. Separately, a conceptual graph is a labeled bipartite graph
whose concept nodes and relation nodes encode typed relations with ordered arguments, while a conceptual
hypergraph represents relation instances as typed hyperedges incident to an ordered tuple of vertices. In this
paper, we extend these conceptual formalisms using the SuperHyperGraph framework, introducing Conceptual
SuperHyperGraphs and examining their basic properties.

Keywords: Conceptual HyperGraph, Conceptual SuperHyperGraph, HyperGraph, SuperHyperGraph