Feature-aware Hypergraph Generation via Next-Scale Prediction

Hypergraphs generalize traditional graphs by allowing hyperedges to connect multiple nodes, making them well-suited for modeling complex structures with higher-order relationships, such as 3D meshes, molecular systems, and electronic circuits. While topology is central to hypergraph structure, many real-world applications also require node and hyperedge features. Existing hypergraph generation methods focus solely on topology, often overlooking feature modeling. In this work, we introduce FAHNES (feature-aware hypergraph generation via next-scale prediction), a hierarchical approach that jointly generates hypergraph topology and features. FAHNES builds a multi-scale representation through node coarsening, then learns to reconstruct finer levels via localized expansion and refinement, guided by a new node budget mechanism that controls cluster splitting. We evaluate FAHNES on synthetic hypergraphs, 3D meshes, and molecular datasets. FAHNES achieves competitive results in reconstructing topology and features, establishing a foundation for future research in featured hypergraph generative modeling.

@article{gailhard2025_2506.01467,
  title={ Feature-aware Hypergraph Generation via Next-Scale Prediction },
  author={ Dorian Gailhard and Enzo Tartaglione and Lirida Naviner and Jhony H. Giraldo },
  journal={arXiv preprint arXiv:2506.01467},
  year={ 2025 }
}