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：超图是强大的数学结构，能够建模社交网络、生物信息学和推荐系统等各个领域中的复杂高阶关系。然而，由于超图固有的复杂性以及缺乏有效的生成模型，生成逼真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方法（HYGENE），该方法通过渐进式局部扩展策略来应对这些挑战。HYGENE基于超图的二分图表示，从单对连接节点出发，通过迭代扩展形成目标超图。在每一步中，利用去噪扩散过程以局部化方式添加节点和超边，从而在细化局部细节之前构建全局结构。我们的实验证明了HYGENE的有效性，展示了其紧密模拟超图中多种属性的能力。据我们所知，这是首次尝试将深度学习模型用于超图生成，我们的工作旨在为该领域的未来研究奠定基础。