raph theory explores the relationships between objects through mathematical structures com-posed of vertices (nodes) and edges (connections). A hypergraph generalizes the classical graph by introducinghyperedges, which can connect any number of vertices rather than just two, thus allowing the modeling of morecomplex multi-way relationships [1]. Building upon this, the concept of a SuperHyperGraph has been introducedas 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 relatedconcepts 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 superhypergraphtheory (cf. [7]). We hope these contributions will promote further development in cognitive modeling and itsapplications across disciplines such as AI, social sciences, and computational sciences.