SuperHype: Hypergraph Generation via Graph-Superposition Decomposition

Hypergraphs are graph generalizations with key applications in domains such as healthcare, where strict data privacy requirements apply, or bioinformatics, where testing new compounds is costly. However, due to their combinatorial nature, hypergraph representations are often either intractable, or introduce major information loss. For this reason, research into hypergraph synthesis is limited, and state-of-the-art approaches yield poor generation quality in terms of overall structural patterns and graph-level validity. To address such shortcomings, we introduce SuperHype, an exact and tractable hypergraph diffusion model. The core of SuperHype is the projection of graph-superposition, a novel representation that embeds a hypergraph into a multilayer graph enabling a tractable representation with no loss of generalization. To generate new samples from such representations, we introduce a Graph-Superposition Transformer that treats the superposition as an interconnected sequence of layers. Moreover, we enhance the model’s performance with hypergraph specific auxiliary features and triplet aggregation of indirect node interactions. Our evaluation on five datasets shows that SuperHype generally reproduces local and global connectivity patterns with superior fidelity than state-of-the-art baselines.