# What Do Graph Convolutional Neural Networks Learn?

arXiv: https://arxiv.org/abs/2207.01839 · HTML: https://mlsanity.com/paper/2207.01839/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 9 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 5 of 5)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervision](https://mlsanity.com/paper/2204.04879/) (2022)
- [DNA-GCN: Graph convolutional networks for predicting DNA-protein binding](https://mlsanity.com/paper/2106.01836/) (2021)

## Built on by (most cited first, 1 of 1)

- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)

## Abstract (arXiv)

Graph neural networks (GNNs) have gained traction over the past few years for their superior performance in numerous machine learning tasks. Graph Convolutional Neural Networks (GCN) are a common variant of GNNs that are known to have high performance in semi-supervised node classification (SSNC), and work well under the assumption of homophily. Recent literature has highlighted that GCNs can achieve strong performance on heterophilous graphs under certain "special conditions". These arguments motivate us to understand why, and how, GCNs learn to perform SSNC. We find a positive correlation between similarity of latent node embeddings of nodes within a class and the performance of a GCN. Our investigation on underlying graph structures of a dataset finds that a GCN's SSNC performance is significantly influenced by the consistency and uniqueness in neighborhood structure of nodes within a class.