# Graph Neural Networks with Heterophily

arXiv: https://arxiv.org/abs/2009.13566 · HTML: https://mlsanity.com/paper/2009.13566/

## Key facts

- Cited by 202 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2020.

## Built on by (most cited first, 30 of 202)

- [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)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations](https://mlsanity.com/paper/2306.10759/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [Not too little, not too much: a theoretical analysis of graph (over)smoothing](https://mlsanity.com/paper/2205.12156/) (2022)
- [Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classification](https://mlsanity.com/paper/2406.08993/) (2024)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [New Benchmarks for Learning on Non-Homophilous Graphs](https://mlsanity.com/paper/2104.01404/) (2021)
- [Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothing](https://mlsanity.com/paper/2302.01524/) (2023)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond](https://mlsanity.com/paper/2209.06177/) (2022)
- [Simplifying approach to Node Classification in Graph Neural Networks](https://mlsanity.com/paper/2111.06748/) (2021)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [TAM: Topology-Aware Margin Loss for Class-Imbalanced Node Classification](https://mlsanity.com/paper/2206.12917/) (2022)
- [Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?](https://mlsanity.com/paper/2306.01323/) (2023)
- [p-Laplacian Based Graph Neural Networks](https://mlsanity.com/paper/2111.07337/) (2021)
- [Tree Decomposed Graph Neural Network](https://mlsanity.com/paper/2108.11022/) (2021)
- [Block Modeling-Guided Graph Convolutional Neural Networks](https://mlsanity.com/paper/2112.13507/) (2021)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [Non-Homophilic Graph Pre-Training and Prompt Learning](https://mlsanity.com/paper/2408.12594/) (2024)
- [Distribution Free Prediction Sets for Node Classification](https://mlsanity.com/paper/2211.14555/) (2022)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.