A wide variety of generative models for graphs have been proposed. They are used in drug discovery, road networks, neural architecture search, and program synthesis. Generating graphs has theoretical challenges, such as isomorphic representations -- evaluating how well a generative model performs is difficult. Which model to choose depending on the application domain? We extensively study kernel-based metrics on distributions of graph invariants and manifold-based and kernel-based metrics in graph embedding space. Manifold-based metrics outperform kernel-based metrics in embedding space. We use these metrics to compare GraphRNN and GRAN, two well-known generative models for graphs, and unveil the influence of node orderings. It shows the superiority of GRAN over GraphRNN - further, our proposed adaptation of GraphRNN with a depth-first search ordering is effective for small-sized graphs. A guideline on good practices regarding dataset selection and node feature initialization is provided. Our work is accompanied by open-source code and reproducible experiments.

翻译：各类图生成模型已被广泛提出，应用于药物发现、道路网络、神经架构搜索及程序合成等领域。图生成面临理论挑战，如需要评估生成模型的同构表示性能——如何评估生成模型的质量存在困难。如何根据应用领域选择模型？我们系统研究了基于图不变量的核度量方法，以及图嵌入空间中基于流形和基于核的度量方法。结果表明，嵌入空间中基于流形的度量优于基于核的度量。利用这些度量，我们对比了两种著名的图生成模型GraphRNN与GRAN，揭示了节点排序的影响。实验显示GRAN优于GraphRNN——此外，我们提出的基于深度优先搜索排序的GraphRNN改进方法对小型图有效。本文提供了关于数据集选择和节点特征初始化的实践指南，并附有开源代码与可复现实验。