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 separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-ofthe-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

翻译：大多数现实世界中的图都展现出层次化结构，而现有图生成方法往往忽视了这一特性。为克服这一局限，我们提出了一种新颖的图生成网络，该网络能够捕捉图的层次化本质，并以从粗到细的方式逐级生成图子结构。在每一层级中，该模型并行生成社区结构，随后通过独立的神经网络预测社区间的交叉边。这种模块化方法实现了大规模复杂图的可扩展生成。此外，我们采用多项分布对层次化图中边的输出分布进行建模，并推导了该分布的递归因子分解形式。这使得我们能够以自回归方式生成具有整数值边权重的社区图。实证研究表明，我们提出的生成模型在效果和可扩展性方面表现优异，在多个基准数据集上均实现了图质量指标的先进性能。代码发布于 https://github.com/Karami-m/HiGen_main。