# Beyond Homophily with Graph Echo State Networks

arXiv: https://arxiv.org/abs/2210.15731 · HTML: https://mlsanity.com/paper/2210.15731/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 27 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [A Gentle Introduction to Deep Learning for Graphs](https://mlsanity.com/paper/1912.12693/) (2019)
- [Fast and Deep Graph Neural Networks](https://mlsanity.com/paper/1911.08941/) (2019)

## Built on by (most cited first, 2 of 2)

- [Leave Graphs Alone: Addressing Over-Squashing without Rewiring](https://mlsanity.com/paper/2212.06538/) (2022)
- [Addressing Heterophily in Node Classification with Graph Echo State Networks](https://mlsanity.com/paper/2305.08233/) (2023)

## Abstract (arXiv)

Graph Echo State Networks (GESN) have already demonstrated their efficacy and efficiency in graph classification tasks. However, semi-supervised node classification brought out the problem of over-smoothing in end-to-end trained deep models, which causes a bias towards high homophily graphs. We evaluate for the first time GESN on node classification tasks with different degrees of homophily, analyzing also the impact of the reservoir radius. Our experiments show that reservoir models are able to achieve better or comparable accuracy with respect to fully trained deep models that implement ad hoc variations in the architectural bias, with a gain in terms of efficiency.