Cognitive HyperGraphs and SuperHyperGraphs: A NovelFramework for Complex Relational Modeling

Abstract

Graph theory explores the relationships between objects through mathematical structures com-
posed of vertices (nodes) and edges (connections). A hypergraph generalizes the classical graph by introducing
hyperedges, which can connect any number of vertices rather than just two, thus allowing the modeling of more
complex multi-way relationships [1]. Building upon this, the concept of a SuperHyperGraph has been introduced
as a further extension of hypergraphs and has recently become a subject of active research [2–4].
A cognitive graph is a structure designed to represent mental models of spatial environments, using nodes,
edges, and labels to encode information such as location, direction, and navigational cues [5, 6]. Closely related
concepts include cognitive maps, which are widely studied in fields such as artificial intelligence, social science,
and computer science.
In this paper, we propose two new extended models: the Cognitive HyperGraph and the Cognitive Super-
HyperGraph, which enhance the traditional cognitive graph framework using hypergraph and superhypergraph
theory (cf. [7]). We hope these contributions will promote further development in cognitive modeling and its
applications across disciplines such as AI, social sciences, and computational sciences.