Property HyperGraphs and Property SuperHyperGraphs for Data Analysis

Abstract

Graph theory provides a rigorous mathematical foundation for modeling relationships by representing entities as vertices and their interactions as edges [1,2]. Hypergraphs generalize this paradigm by allowing hyperedges to connect arbitrary subsets of vertices [3], and SuperHyperGraphs extend it further via iterated powerset constructions that capture hierarchical, multi‐layer linkages among edges [4, 5]. These enriched models support applications across biology, social networks, signal processing, and knowledge representation. Property Graphs are directed multigraphs in which vertices and edges carry key–value properties and edges additionally bear labels, enabling schema‐flexible modeling of heterogeneous, real‐world data(cf. [6–8]). In this paper, we show how to elevate Property Graphs to the settings of HyperGraphs and SuperHyperGraphs by introducing formal definitions for Property HyperGraphs and Property SuperHyperGraphs and presenting preliminary theoretical results that demonstrate their expressive power.