# Disentangling Homophily and Rarity: Explaining Failure in Graph Neural Networks

arXiv: https://arxiv.org/abs/2608.14823 · HTML: https://mlsanity.com/paper/2608.14823/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 14 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [SAMGPT: Text-free Graph Foundation Model for Multi-domain Pre-training and Cross-domain Adaptation](https://mlsanity.com/paper/2502.05424/) (2025)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [A Closer Look at Classification Evaluation Metrics and a Critical Reflection of Common Evaluation Practice](https://mlsanity.com/paper/2404.16958/) (2024)
- [Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approach](https://mlsanity.com/paper/2406.03464/) (2024)
- [On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networks](https://mlsanity.com/paper/2306.05557/) (2023)
- [Probing Graph Representations](https://mlsanity.com/paper/2303.03951/) (2023)
- [Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts](https://mlsanity.com/paper/2408.09490/) (2024)
- [Unveiling the Impact of Local Homophily on GNN Fairness: In-Depth Analysis and New Benchmarks](https://mlsanity.com/paper/2410.04287/) (2024)
- [Standardization and Control for Confounding in Observational Studies: A Historical Perspective](https://mlsanity.com/paper/1503.02853/) (2015)
- [Fine-Grained Class-Conditional Distribution Balancing for Debiased Learning](https://mlsanity.com/paper/2505.06831/) (2025)
- [SCL-GNN: Towards Generalizable Graph Neural Networks via Spurious Correlation Learning](https://mlsanity.com/paper/2603.08270/) (2026)

## Abstract (arXiv)

Are heterophilic nodes in a graph harder to classify because they are heterophilic or because they are rare? Some existing work frames classification of such nodes as a subgroup generalisation problem, where a model performs well on the majority group at the expense of the rare group. Others explain this as a problem of neighbourhood aggregation in graph neural networks (GNNs). We assess these two viewpoints through a detailed evaluation of six GNNs on five datasets of varying homophily, and find that homophilic nodes tend to be easier to classify, even when they are rare---challenging the subgroup framing. However, our findings also nuance existing beliefs about how GNNs misrepresent heterophilic nodes. We demonstrate that the information needed to classify heterophilic nodes correctly is often recoverable by retraining the classification head of a model, or even just the final linear classification layer.