# Implicit Graphon Neural Representation

arXiv: https://arxiv.org/abs/2211.03329 · HTML: https://mlsanity.com/paper/2211.03329/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [GraphVAE: Towards Generation of Small Graphs Using Variational Autoencoders](https://mlsanity.com/paper/1802.03480/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [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)
- [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)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [Learning Graphons via Structured Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2012.05644/) (2020)
- [Online Graph Dictionary Learning](https://mlsanity.com/paper/2102.06555/) (2021)
- [Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning](https://mlsanity.com/paper/1708.01955/) (2017)
- [Gromov-Wasserstein Factorization Models for Graph Clustering](https://mlsanity.com/paper/1911.08530/) (2019)
- [Learning to Predict Graphs with Fused Gromov-Wasserstein Barycenters](https://mlsanity.com/paper/2202.03813/) (2022)
- [The Geometry of Continuous Latent Space Models for Network Data](https://mlsanity.com/paper/1712.08641/) (2017)
- [Graphons, mergeons, and so on!](https://mlsanity.com/paper/1607.01718/) (2016)
- [Learning Graphon Autoencoders for Generative Graph Modeling](https://mlsanity.com/paper/2105.14244/) (2021)

## Built on by (most cited first, 19 of 19)

- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Graph Neural Tangent Kernel: Convergence on Large Graphs](https://mlsanity.com/paper/2301.10808/) (2023)
- [Scalable Implicit Graphon Learning](https://mlsanity.com/paper/2410.17464/) (2024)
- [Attention Beats Linear for Fast Implicit Neural Representation Generation](https://mlsanity.com/paper/2407.15355/) (2024)
- [Nonparametric Teaching for Graph Property Learners](https://mlsanity.com/paper/2505.14170/) (2025)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Prior-Informed Flow Matching for Graph Reconstruction](https://mlsanity.com/paper/2601.22107/) (2026)
- [A Few Moments Please: Scalable Graphon Learning via Moment Matching](https://mlsanity.com/paper/2506.04206/) (2025)
- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)
- [The Graphon Limit Hypothesis: Understanding Neural Network Pruning via Infinite Width Analysis](https://mlsanity.com/paper/2510.17515/) (2025)
- [On the Convergence and Size Transferability of Continuous-depth Graph Neural Networks](https://mlsanity.com/paper/2510.03923/) (2025)
- [Transfer Learning on Edge Connecting Probability Estimation under Graphon Model](https://mlsanity.com/paper/2510.05527/) (2025)
- [DiPhon: Diffusion on Graphons for Scalable Graph Generation](https://mlsanity.com/paper/2607.07232/) (2026)
- [Extending Graph Condensation to Multi-Label Datasets: A Benchmark Study](https://mlsanity.com/paper/2412.17961/) (2024)
- [Model-Driven Graph Contrastive Learning](https://mlsanity.com/paper/2506.06212/) (2025)
- [From Moments to Models: Graphon-Mixture Learning for Mixup and Contrastive Learning](https://mlsanity.com/paper/2510.03690/) (2025)
- [Low-Complexity and Consistent Graphon Estimation from Multiple Networks](https://mlsanity.com/paper/2603.15578/) (2026)
- [Attention Graphons: A Graph Limit Perspective on Graph Transformers](https://mlsanity.com/paper/2609.35620/) (2026)
- [A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators](https://mlsanity.com/paper/2610.02439/) (2026)

## Abstract (arXiv)

Graphons are general and powerful models for generating graphs of varying size. In this paper, we propose to directly model graphons using neural networks, obtaining Implicit Graphon Neural Representation (IGNR). Existing work in modeling and reconstructing graphons often approximates a target graphon by a fixed resolution piece-wise constant representation. Our IGNR has the benefit that it can represent graphons up to arbitrary resolutions, and enables natural and efficient generation of arbitrary sized graphs with desired structure once the model is learned. Furthermore, we allow the input graph data to be unaligned and have different sizes by leveraging the Gromov-Wasserstein distance. We first demonstrate the effectiveness of our model by showing its superior performance on a graphon learning task. We then propose an extension of IGNR that can be incorporated into an auto-encoder framework, and demonstrate its good performance under a more general setting of graphon learning. We also show that our model is suitable for graph representation learning and graph generation.