# Graphon Filters: Graph Signal Processing in the Limit

arXiv: https://arxiv.org/abs/2003.02099 · HTML: https://mlsanity.com/paper/2003.02099/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 16 of 16)

- [Transferability of Graph Neural Networks: an Extended Graphon Approach](https://mlsanity.com/paper/2109.10096/) (2021)
- [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)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphs](https://mlsanity.com/paper/2212.08171/) (2022)
- [Learning Graphon Autoencoders for Generative Graph Modeling](https://mlsanity.com/paper/2105.14244/) (2021)
- [Sampling and Uniqueness Sets in Graphon Signal Processing](https://mlsanity.com/paper/2401.06279/) (2024)
- [Transferability of Graph Neural Networks using Graphon and Sampling Theories](https://mlsanity.com/paper/2307.13206/) (2023)
- [Convolutional Filtering with RKHS Algebras](https://mlsanity.com/paper/2411.01341/) (2024)
- [Learning graphons from data: Random walks, transfer operators, and spectral clustering](https://mlsanity.com/paper/2507.18147/) (2025)
- [Transferable Graphical MARL for Real-Time Estimation in Dynamic Wireless Networks](https://mlsanity.com/paper/2404.03227/) (2024)
- [On the Convergence and Size Transferability of Continuous-depth Graph Neural Networks](https://mlsanity.com/paper/2510.03923/) (2025)
- [RKHS Representation of Algebraic Convolutional Filters with Integral Operators](https://mlsanity.com/paper/2602.19094/) (2026)
- [Spectral Convergence of Complexon Shift Operators](https://mlsanity.com/paper/2309.07169/) (2023)
- [Decentralized Learning Strategies for Estimation Error Minimization with Graph Neural Networks](https://mlsanity.com/paper/2601.12662/) (2026)
- [Fundamental Limits of Transferability and Equivariance in Algebraic Signal Models I: Finite Dimensions](https://mlsanity.com/paper/2609.36106/) (2026)

## Abstract (arXiv)

Graph signal processing is an emerging field which aims to model processes that exist on the nodes of a network and are explained through diffusion over this structure. Graph signal processing works have heretofore assumed knowledge of the graph shift operator. Our approach is to investigate the question of graph filtering on a graph about which we only know a model. To do this we leverage the theory of graphons proposed by L. Lovasz and B. Szegedy. We make three key contributions to the emerging field of graph signal processing. We show first that filters defined over the scaled adjacency matrix of a random graph drawn from a graphon converge to filters defined over the Fredholm integral operator with the graphon as its kernel. Second, leveraging classical findings from the theory of the numerical solution of Fredholm integral equations, we define the Fourier-Galerkin shift operator. Lastly, using the Fourier-Galerkin shift operator, we derive a graph filter design algorithm which only depends on the graphon, and thus depends only on the probabilistic structure of the graph instead of the particular graph itself. The derived graphon filtering algorithm is verified through simulations on a variety of random graph models.