# Scalable Implicit Graphon Learning

arXiv: https://arxiv.org/abs/2410.17464 · HTML: https://mlsanity.com/paper/2410.17464/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 46 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 20 of 20)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [G-Mixup: Graph Data Augmentation for Graph Classification](https://mlsanity.com/paper/2202.07179/) (2022)
- [Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matching](https://mlsanity.com/paper/1905.07645/) (2019)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [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)
- [Link Scheduling using Graph Neural Networks](https://mlsanity.com/paper/2109.05536/) (2021)
- [Implicit Graphon Neural Representation](https://mlsanity.com/paper/2211.03329/) (2022)
- [Private Graphon Estimation for Sparse Graphs](https://mlsanity.com/paper/1506.06162/) (2015)
- [Centrality measures for graphons: Accounting for uncertainty in networks](https://mlsanity.com/paper/1707.09350/) (2017)
- [GraphMAD: Graph Mixup for Data Augmentation using Data-Driven Convex Clustering](https://mlsanity.com/paper/2210.15721/) (2022)
- [Graphon Control of Large-scale Networks of Linear Systems](https://mlsanity.com/paper/1807.03412/) (2018)
- [Network Topology Inference with Graphon Spectral Penalties](https://mlsanity.com/paper/2010.07872/) (2020)
- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [GraSSRep: Graph-Based Self-Supervised Learning for Repeat Detection in Metagenomic Assembly](https://mlsanity.com/paper/2402.09381/) (2024)

## Built on by (most cited first, 9 of 9)

- [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)
- [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)
- [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)
- [Feasible Flow Matching for Graph Reconstruction via Within-Sampling Primal-Dual Guidance](https://mlsanity.com/paper/2609.32980/) (2026)
- [A Generative Model of Complex Networks Using Graphons and Neural Inverse Operators](https://mlsanity.com/paper/2610.02439/) (2026)

## Abstract (arXiv)

Graphons are continuous models that represent the structure of graphs and allow the generation of graphs of varying sizes. We propose Scalable Implicit Graphon Learning (SIGL), a scalable method that combines implicit neural representations (INRs) and graph neural networks (GNNs) to estimate a graphon from observed graphs. Unlike existing methods, which face important limitations like fixed resolution and scalability issues, SIGL learns a continuous graphon at arbitrary resolutions. GNNs are used to determine the correct node ordering, improving graph alignment. Furthermore, we characterize the asymptotic consistency of our estimator, showing that more expressive INRs and GNNs lead to consistent estimators. We evaluate SIGL in synthetic and real-world graphs, showing that it outperforms existing methods and scales effectively to larger graphs, making it ideal for tasks like graph data augmentation.