In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates community structures at multiple resolutions, with the generated structures conforming to training data distribution at each level of the hierarchy. The graphs generation is designed as a sequence of coarse-to-fine generative models allowing for parallel generation of all sub-structures, resulting in a high degree of scalability. Furthermore, we model the output distribution of edges with a more expressive multinomial distribution and derive a recursive factorization for this distribution, making it a suitable choice for graph generative models. This allows for the generation of graphs with integer-valued edge weights. Our method achieves state-of-the-art performance in both accuracy and efficiency on multiple datasets.

翻译：在现实世界中，大多数图自然具有层次结构。然而，基于数据的图生成方法尚未有效捕捉此类结构。为此，我们提出一种新颖方法，通过递归地在多个分辨率下生成社区结构，使生成的每个层级结构符合训练数据分布。图生成过程被设计为从粗到细的生成模型序列，允许所有子结构并行生成，从而具备高度可扩展性。此外，我们采用更具表现力的多项分布对边输出分布进行建模，并推导出该分布的递归分解形式，使其成为图生成模型的理想选择，从而能够生成具有整数边权的图。我们的方法在多个数据集上实现了准确性和效率方面的最佳性能。