Generating real-world hypergraphs via deep generative models

Hypergraph generation has found wide applications in data analysis, social networks, and communication networks. Although various hypergraph generation methods have been proposed, many challenges remain. On the one hand, traditional hypergraph generation methods are time-consuming since they rely on computing various statistics about hypergraph distributions prior to generation. On the other hand, they store many intermediate variables in the process of hypergraph generation, thus depleting a large number of memory resources, which could lead to memory explosion. To address these issues, we present a novel deep generative model for hypergraph generation (DGMH), which consists of a node selection module and a hyperedge size decision module. In DGMH, each hyperedge is treated as an embedding in a high-dimensional space, where values along specific dimensions represent the probabilities of node inclusion in the hyperedge. The node selection module captures the distribution of hyperedge embeddings and identifies other latent hyperedge embeddings within the space. In addition, the hyperedge size decision module determines the hyperedge size based on the hyperedge embedding. We sample a certain number of nodes from the categorical distribution parameterized by the embedding and assign these nodes to the hyperedge, an essential step in hyperedge generation. Once a sufficient number of hyperedges are generated, they are connected through common nodes to form a complete hypergraph. Experimental results demonstrate the effectiveness of DGMH in capturing the structural distribution of hypergraphs in a short time while maintaining a modest memory footprint during the generation process.