HYGENE: A Diffusion-based Hypergraph Generation Method

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.

💡 Research Summary

The paper introduces HYGENE, the first diffusion‑based method for generating hypergraphs. Hypergraphs, which can model high‑order relationships, have been difficult to generate realistically because of the combinatorial explosion of possible hyperedges and the lack of deep‑learning‑based generative models. HYGENE tackles these challenges by (1) representing a hypergraph simultaneously as a weighted clique expansion and as a bipartite “star” graph, and (2) employing a progressive local expansion scheme that mirrors the coarsening‑refinement cycle used in recent graph generation work.

During training, the weighted clique expansion is repeatedly coarsened using a spectral‑preserving graph coarsening algorithm (adapted from Loukas