HiGen: Hierarchical Graph Generative Networks

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using a separate model. This modular approach results in a highly scalable graph generative network. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution, enabling us to generate sub-graphs with integer-valued edge weights in an autoregressive approach. Empirical studies demonstrate that the proposed generative model can effectively capture both local and global properties of graphs and achieves state-of-the-art performance in terms of graph quality on various benchmarks.