# Generalized Graphon Process: Convergence of Graph Frequencies in Stretched Cut Distance

arXiv: https://arxiv.org/abs/2309.05260 · HTML: https://mlsanity.com/paper/2309.05260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 11 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graphon Neural Networks and the Transferability of Graph Neural Networks](https://mlsanity.com/paper/2006.03548/) (2020)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Graphon Signal Processing](https://mlsanity.com/paper/2003.05030/) (2020)
- [On the Robustness of Graph Neural Diffusion to Topology Perturbations](https://mlsanity.com/paper/2209.07754/) (2022)
- [On the Transferability of Spectral Graph Filters](https://mlsanity.com/paper/1901.10524/) (2019)
- [The Graphon Fourier Transform](https://mlsanity.com/paper/1910.10195/) (2019)
- [On Local Distributions in Graph Signal Processing](https://mlsanity.com/paper/2202.10649/) (2022)

## Abstract (arXiv)

Graphons have traditionally served as limit objects for dense graph sequences, with the cut distance serving as the metric for convergence. However, sparse graph sequences converge to the trivial graphon under the conventional definition of cut distance, which make this framework inadequate for many practical applications. In this paper, we utilize the concepts of generalized graphons and stretched cut distance to describe the convergence of sparse graph sequences. Specifically, we consider a random graph process generated from a generalized graphon. This random graph process converges to the generalized graphon in stretched cut distance. We use this random graph process to model the growing sparse graph, and prove the convergence of the adjacency matrices' eigenvalues. We supplement our findings with experimental validation. Our results indicate the possibility of transfer learning between sparse graphs.