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.

研究比较了基于核方法和流形方法的度量方法，发现流形方法在图嵌入空间中优于核方法；在此基础上运用这些度量方法比较了两个常见的图生成模型 GraphRNN 和 GRAN，揭示了节点排序的影响，发现 GRAN 比 GraphRNN 更优，作者的新算法对小型图效果更好。研究还提供了关于数据集选择和节点特征初始化的良好实践指南，并且有开放源代码与可再生实验。