Dorian Gailhard

Dorian Gailhard, Enzo Tartaglione, Lirida Naviner et al.

Hypergraphs are powerful mathematical structures that can model complex, high-order relationships in various domains, including social networks, bioinformatics, and recommender systems. However, generating realistic and diverse hypergraphs remains challenging due to their inherent complexity and lack of effective generative models. In this paper, we introduce a diffusion-based Hypergraph Generation (HYGENE) method that addresses these challenges through a progressive local expansion approach. HYGENE works on the bipartite representation of hypergraphs, starting with a single pair of connected nodes and iteratively expanding it to form the target hypergraph. At each step, nodes and hyperedges are added in a localized manner using a denoising diffusion process, which allows for the construction of the global structure before refining local details. Our experiments demonstrated the effectiveness of HYGENE, proving its ability to closely mimic a variety of properties in hypergraphs. To the best of our knowledge, this is the first attempt to employ deep learning models for hypergraph generation, and our work aims to lay the groundwork for future research in this area.

Dorian Gailhard, Enzo Tartaglione, Lirida Naviner et al.

Graph generative models have shown strong results in molecular design but struggle to scale to large, complex structures. While hierarchical methods improve scalability, they usually ignore node and edge features, which are critical in real-world applications. This issue is amplified in hypergraphs, where hyperedges capture higher-order relationships among multiple nodes. Despite their importance in domains such as 3D geometry, molecular systems, and circuit design, existing generative models rarely support both hypergraphs and feature generation at scale. In this paper, we introduce FAHNES (feature-aware hypergraph generation via next-scale prediction), a hierarchical framework that jointly generates hypergraph topology and features. FAHNES builds multi-scale representations through node coarsening and refines them via localized expansion, guided by a novel node budget mechanism that controls granularity and ensures consistency across scales. Experiments on synthetic, 3D mesh and graph point cloud datasets show that FAHNES achieves state-of-the-art performance in jointly generating features and structure, advancing scalable hypergraph and graph generation.