Knowledge SuperHypergraphs, Multimodal SuperHypergraphs, Lattice SuperHypergraphs, and Hyperbolic SuperHypergraphs: Concepts and Applications

This work builds on hypergraphs-graphs whose edges can link any number of vertices-and superhypergraphs, which add a recursive, hierarchical powerset structure to hyperedges.It reviews four practical hypergraph variants: Knowledge Hypergraphs (for multi-relational knowledge representation), Multimodal Hypergraphs (for combining different data modalities), Lattice Hypergraphs (for spatial and topological modeling), and Hyperbolic Hypergraphs (for embedding vertices in hyperbolic space to capture hierarchies).The paper then shows how to elevate each of these into the superhypergraph framework-resulting in Knowledge SuperHypergraphs, Multimodal SuperHypergraphs, Lattice SuperHypergraphs, and Hyperbolic SuperHypergraphs-and outlines their core properties.Overall, it offers a unified, more expressive modeling approach that paves the way for future advances in both hypergraph and superhypergraph research.