# The Graphon Fourier Transform

arXiv: https://arxiv.org/abs/1910.10195 · HTML: https://mlsanity.com/paper/1910.10195/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2019.

## Built on by (most cited first, 10 of 10)

- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Transferability Properties of Graph Neural Networks](https://mlsanity.com/paper/2112.04629/) (2021)
- [Learning by Transference: Training Graph Neural Networks on Growing Graphs](https://mlsanity.com/paper/2106.03693/) (2021)
- [Learning Graphon Autoencoders for Generative Graph Modeling](https://mlsanity.com/paper/2105.14244/) (2021)
- [Training Graph Neural Networks on Growing Stochastic Graphs](https://mlsanity.com/paper/2210.15567/) (2022)
- [A Poincar'e Inequality and Consistency Results for Signal Sampling on Large Graphs](https://mlsanity.com/paper/2311.10610/) (2023)
- [Generalized Graphon Process: Convergence of Graph Frequencies in Stretched Cut Distance](https://mlsanity.com/paper/2309.05260/) (2023)
- [Spectral Convergence of Complexon Shift Operators](https://mlsanity.com/paper/2309.07169/) (2023)
- [Graph Semi-Supervised Learning for Point Classification on Data Manifolds](https://mlsanity.com/paper/2506.12197/) (2025)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be redesigned. To address this, we consider graphons, which are both limit objects of convergent graph sequences and random graph models. We define graphon signals and introduce the Graphon Fourier Transform (WFT), to which the Graph Fourier Transform (GFT) is shown to converge. This result is demonstrated in two numerical experiments where, as expected, the GFT converges, hinting to the possibility of centralizing analysis and design on graphons to leverage transferability.