# Graphons: A Nonparametric Method to Model, Estimate, and Design Algorithms for Massive Networks

arXiv: https://arxiv.org/abs/1706.01143 · HTML: https://mlsanity.com/paper/1706.01143/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2017.

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

- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Convolutional Neural Networks on Manifolds: From Graphs and Back](https://mlsanity.com/paper/2210.00376/) (2022)
- [Fine-tuning Graph Neural Networks by Preserving Graph Generative Patterns](https://mlsanity.com/paper/2312.13583/) (2023)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [Private Edge Density Estimation for Random Graphs: Optimal, Efficient and Robust](https://mlsanity.com/paper/2405.16663/) (2024)
- [Modularity maximisation for graphons](https://mlsanity.com/paper/2101.00503/) (2021)
- [A Poincar'e Inequality and Consistency Results for Signal Sampling on Large Graphs](https://mlsanity.com/paper/2311.10610/) (2023)
- [Graph Semi-Supervised Learning for Point Classification on Data Manifolds](https://mlsanity.com/paper/2506.12197/) (2025)
- [A Generative Model for Controllable Feature Heterophily in Graphs](https://mlsanity.com/paper/2509.23230/) (2025)

## Abstract (arXiv)

Many social and economic systems are naturally represented as networks, from off-line and on-line social networks, to bipartite networks, like Netflix and Amazon, between consumers and products. Graphons, developed as limits of graphs, form a natural, nonparametric method to describe and estimate large networks like Facebook and LinkedIn. Here we describe the development of the theory of graphons, for both dense and sparse networks, over the last decade. We also review theorems showing that we can consistently estimate graphons from massive networks in a wide variety of models. Finally, we show how to use graphons to estimate missing links in a sparse network, which has applications from estimating social and information networks in development economics, to rigorously and efficiently doing collaborative filtering with applications to movie recommendations in Netflix and product suggestions in Amazon.