Directed SuperHyperGraph Neural Networks
Takaaki Fujita · 2025
Graph theory provides a mathematical framework for representing relationships between entities as vertices (nodes) connected by edges [1-3]. A hypergraph extends this notion by allowing hyperedges to incident on any number of vertices, thereby capturing complex multi-way interactions [4,5]. The concept of a SuperHyperGraph further generalizes hypergraphs through iterated power-set constructions and has recently attracted significant research interest [6,7]. In addition to undirected graphs, there exist directed, bidirected [8], and multidirected [9] variants that encode richer orientation information. Graph Neural Networks (GNNs) have emerged as a powerful tool in artificial intelligence for learning on structured data [10-13]. Recent work has extended GNNs to directed graphs, and research has begun to explore Directed HyperGraph Neural Networks. Undirected SuperHyperGraph Neural Networks have likewise been investigated [14]. In this paper, we introduce the Directed 𝑛-SuperHyperGraph Neural Network, which unifies the Directed HyperGraph Neural Network and the 𝑛-SuperHyperGraph Neural Network into a cohesive architecture. We anticipate that this novel model will advance the state of the art in GNN research.