# Learning Graphon Autoencoders for Generative Graph Modeling

arXiv: https://arxiv.org/abs/2105.14244 · HTML: https://mlsanity.com/paper/2105.14244/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 70 references that are in the map.
- First posted on arXiv 29 May 2021.

## Builds on (most cited first, 30 of 43)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [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)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Order Matters: Sequence to sequence for sets](https://mlsanity.com/paper/1511.06391/) (2015)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [Hierarchical Generation of Molecular Graphs using Structural Motifs](https://mlsanity.com/paper/2002.03230/) (2020)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Reward Augmented Maximum Likelihood for Neural Structured Prediction](https://mlsanity.com/paper/1609.00150/) (2016)
- [Scalable Deep Generative Modeling for Sparse Graphs](https://mlsanity.com/paper/2006.15502/) (2020)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [Topic-Guided Variational Autoencoders for Text Generation](https://mlsanity.com/paper/1903.07137/) (2019)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)

## Built on by (most cited first, 5 of 5)

- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [When to Pre-Train Graph Neural Networks? From Data Generation Perspective!](https://mlsanity.com/paper/2303.16458/) (2023)
- [Fused Gromov-Wasserstein Graph Mixup for Graph-level Classifications](https://mlsanity.com/paper/2306.15963/) (2023)
- [DiPhon: Diffusion on Graphons for Scalable Graph Generation](https://mlsanity.com/paper/2607.07232/) (2026)
- [A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators](https://mlsanity.com/paper/2610.02439/) (2026)

## Abstract (arXiv)

Graphon is a nonparametric model that generates graphs with arbitrary sizes and can be induced from graphs easily. Based on this model, we propose a novel algorithmic framework called textitgraphon autoencoder to build an interpretable and scalable graph generative model. This framework treats observed graphs as induced graphons in functional space and derives their latent representations by an encoder that aggregates Chebshev graphon filters. A linear graphon factorization model works as a decoder, leveraging the latent representations to reconstruct the induced graphons (and the corresponding observed graphs). We develop an efficient learning algorithm to learn the encoder and the decoder, minimizing the Wasserstein distance between the model and data distributions. This algorithm takes the KL divergence of the graph distributions conditioned on different graphons as the underlying distance and leads to a reward-augmented maximum likelihood estimation. The graphon autoencoder provides a new paradigm to represent and generate graphs, which has good generalizability and transferability.