# Beyond MMD: Evaluating Graph Generative Models with Geometric Deep Learning

arXiv: https://arxiv.org/abs/2512.14241 · HTML: https://mlsanity.com/paper/2512.14241/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 45 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 23 of 23)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [A Systematic Survey on Deep Generative Models for Graph Generation](https://mlsanity.com/paper/2007.06686/) (2020)
- [Efficient and Degree-Guided Graph Generation via Discrete Diffusion Modeling](https://mlsanity.com/paper/2305.04111/) (2023)
- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Deep Graph Similarity Learning: A Survey](https://mlsanity.com/paper/1912.11615/) (2019)
- [Machine learning dismantling and early-warning signals of disintegration in complex systems](https://mlsanity.com/paper/2101.02453/) (2021)
- [Emergence of Soft Communities from Geometric Preferential Attachment](https://mlsanity.com/paper/1501.06835/) (2015)
- [wsGAT: Weighted and Signed Graph Attention Networks for Link Prediction](https://mlsanity.com/paper/2109.11519/) (2021)
- [CGMN: A Contrastive Graph Matching Network for Self-Supervised Graph Similarity Learning](https://mlsanity.com/paper/2205.15083/) (2022)
- [Solving the Problem of the K Parameter in the KNN Classifier Using an Ensemble Learning Approach](https://mlsanity.com/paper/1409.0919/) (2014)
- [A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities](https://mlsanity.com/paper/1707.07325/) (2017)

## Built on by (most cited first, 1 of 1)

- [ProtoGuide: Prototype-Driven Guidance for Class-Conditional Graph Generation](https://mlsanity.com/paper/2609.15239/) (2026)

## Abstract (arXiv)

Graph generation is a crucial task in many fields, including network science and bioinformatics, as it enables the creation of synthetic graphs that mimic the properties of real-world networks for various applications. Graph Generative Models (GGMs) have emerged as a promising solution to this problem, leveraging deep learning techniques to learn the underlying distribution of real-world graphs and generate new samples that closely resemble them. Examples include approaches based on Variational Auto-Encoders, Recurrent Neural Networks, and more recently, diffusion-based models. However, the main limitation often lies in the evaluation process, which typically relies on Maximum Mean Discrepancy (MMD) as a metric to assess the distribution of graph properties in the generated ensemble. This paper introduces a novel methodology for evaluating GGMs that overcomes the limitations of MMD, which we call RGM (Representation-aware Graph-generation Model evaluation). As a practical demonstration of our methodology, we present a comprehensive evaluation of two state-of-the-art Graph Generative Models: Graph Recurrent Attention Networks (GRAN) and Efficient and Degree-guided graph GEnerative model (EDGE). We investigate their performance in generating realistic graphs and compare them using a Geometric Deep Learning model trained on a custom dataset of synthetic and real-world graphs, specifically designed for graph classification tasks. Our findings reveal that while both models can generate graphs with certain topological properties, they exhibit significant limitations in preserving the structural characteristics that distinguish different graph domains. We also highlight the inadequacy of Maximum Mean Discrepancy as an evaluation metric for GGMs and suggest alternative approaches for future research.