# GRAN is superior to GraphRNN: node orderings, kernel- and graph embeddings-based metrics for graph generators

arXiv: https://arxiv.org/abs/2307.06709 · HTML: https://mlsanity.com/paper/2307.06709/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 13 Jul 2023.

## Builds on (most cited first, 18 of 18)

- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [Learning Deep Generative Models of Graphs](https://mlsanity.com/paper/1803.03324/) (2018)
- [The Surprising Power of Graph Neural Networks with Random Node Initialization](https://mlsanity.com/paper/2010.01179/) (2020)
- [Random Features Strengthen Graph Neural Networks](https://mlsanity.com/paper/2002.03155/) (2020)
- [NetGAN: Generating Graphs via Random Walks](https://mlsanity.com/paper/1803.00816/) (2018)
- [GraphGen: A Scalable Approach to Domain-agnostic Labeled Graph Generation](https://mlsanity.com/paper/2001.08184/) (2020)
- [On Positional and Structural Node Features for Graph Neural Networks on Non-attributed Graphs](https://mlsanity.com/paper/2107.01495/) (2021)
- [On Evaluation Metrics for Graph Generative Models](https://mlsanity.com/paper/2201.09871/) (2022)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Building LEGO Using Deep Generative Models of Graphs](https://mlsanity.com/paper/2012.11543/) (2020)
- [DeepGG: a Deep Graph Generator](https://mlsanity.com/paper/2006.04159/) (2020)

## Built on by (most cited first, 2 of 2)

- [Data Augmentation in Graph Neural Networks: The Role of Generated Synthetic Graphs](https://mlsanity.com/paper/2407.14765/) (2024)
- [GraphRNN Revisited: An Ablation Study and Extensions for Directed Acyclic Graphs](https://mlsanity.com/paper/2307.14109/) (2023)

## Abstract (arXiv)

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.