Medical Knowledge Hypergraphs and Medical Knowledge Superhypergraphs

Abstract

A finite hypergraph extends the classical graph model by allowing hyperedges that may connect any nonempty subset of vertices [1, 2, 3]. Building on this foundation, a finite SuperHyperGraph is obtained by iteratively applying the powerset construction, thereby forming nested families of vertex and edge sets that encode multi-layered relationships [4, 5]. A Knowledge Graph is a graph-based representation that encodes facts as entities together with their relations, supporting reasoning, semantic search, and knowledge-driven applications. A Medical Knowledge Graph adapts this paradigm to the medical domain, modeling entities such as diseases, symptoms, drugs, and procedures, and linking them through clinically meaningful relations to facilitate decision support. In this paper, we extend the Medical Knowledge Graph framework using HyperGraphs and SuperHyperGraphs, and investigate its properties. A Medical Knowledge HyperGraph further generalizes the framework by permitting hyperedges that simultaneously connect multiple medical entities, thereby capturing complex clinical relationships not representable with simple triples. Finally, a Medical Knowledge
SuperHyperGraph introduces hierarchical layers via iterated powersets, enabling the representation of multi-level medical relations and providing a unifying model that encompasses graphs, hypergraphs, and typed medical knowledge structures.