Toward a Unified Theory of Brain Hypergraphs and Symptom Hypernetworks in Medicine and Neuroscience

Abstract

Many biomedical systems exhibit interactions that go beyond simple pairwise connections. A hypergraph generalizes a graph by permitting an edge to connect any number of vertices—such edges are called hyperedges. A superhypergraph further extends this concept by recursively nesting powerset layers, enabling multi-level and self-referential relationships. In neuroscience, Brain Graphs represent pairwise functional or structural connectivity among brain regions, while Symptom Networks capture statistical dependencies among clinical symptoms. In this work, We propose four novel frameworks—Brain Hypergraphs, Symptom Hypernetworks, Brain Superhypergraphs, and Symptom Superhypernetworks. For each, We provide rigorous definitions, illustrative examples drawn from real-world biomedical scenarios, and an analysis of their core mathematical properties. These advanced models are specifically designed to represent complex, multi-way, and hierarchical interactions that classical graphs cannot capture. This paper is devoted to the theoretical formulation and property analysis of these new network structures. We anticipate that future research will implement these frameworks computationally and validate them with domain experts to unlock deeper insights into brain function and disease symptomatology.