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.

翻译：超图是一种强大的数学结构，能够对社交网络、生物信息学和推荐系统等多个领域中复杂的高阶关系进行建模。然而，由于其固有的复杂性以及缺乏有效的生成模型，生成真实且多样化的超图仍然具有挑战性。本文提出了一种基于扩散的超图生成（HYGENE）方法，该方法通过渐进式局部扩展策略应对这些挑战。HYGENE 在超图的二分图表示上操作，从单个连接的节点对开始，迭代扩展以形成目标超图。在每一步中，节点和超边通过去噪扩散过程以局部化的方式添加，这使得在细化局部细节之前能够构建全局结构。我们的实验证明了 HYGENE 的有效性，证实了其能够紧密模拟超图中的多种特性。据我们所知，这是首次尝试使用深度学习模型进行超图生成，我们的工作旨在为该领域的未来研究奠定基础。