# GCNH: A Simple Method For Representation Learning On Heterophilous Graphs

arXiv: https://arxiv.org/abs/2304.10896 · HTML: https://mlsanity.com/paper/2304.10896/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 21 Apr 2023.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [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)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [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)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Node Similarity Preserving Graph Convolutional Networks](https://mlsanity.com/paper/2011.09643/) (2020)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophily](https://mlsanity.com/paper/2110.15777/) (2021)
- [Improving Graph Neural Networks with Simple Architecture Design](https://mlsanity.com/paper/2105.07634/) (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)
- [2-hop Neighbor Class Similarity (2NCS): A graph structural metric indicative of graph neural network performance](https://mlsanity.com/paper/2212.13202/) (2022)

## Built on by (most cited first, 4 of 4)

- [Deep learning for dynamic graphs: models and benchmarks](https://mlsanity.com/paper/2307.06104/) (2023)
- [Variational Graph Auto-Encoder Based Inductive Learning Method for Semi-Supervised Classification](https://mlsanity.com/paper/2403.17500/) (2024)
- [Transfer Entropy in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2406.06632/) (2024)
- [MHSA: A Multi-scale Hypergraph Network for Mild Cognitive Impairment Detection via Synchronous and Attentive Fusion](https://mlsanity.com/paper/2412.12149/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are well-suited for learning on homophilous graphs, i.e., graphs in which edges tend to connect nodes of the same type. Yet, achievement of consistent GNN performance on heterophilous graphs remains an open research problem. Recent works have proposed extensions to standard GNN architectures to improve performance on heterophilous graphs, trading off model simplicity for prediction accuracy. However, these models fail to capture basic graph properties, such as neighborhood label distribution, which are fundamental for learning. In this work, we propose GCN for Heterophily (GCNH), a simple yet effective GNN architecture applicable to both heterophilous and homophilous scenarios. GCNH learns and combines separate representations for a node and its neighbors, using one learned importance coefficient per layer to balance the contributions of center nodes and neighborhoods. We conduct extensive experiments on eight real-world graphs and a set of synthetic graphs with varying degrees of heterophily to demonstrate how the design choices for GCNH lead to a sizable improvement over a vanilla GCN. Moreover, GCNH outperforms state-of-the-art models of much higher complexity on four out of eight benchmarks, while producing comparable results on the remaining datasets. Finally, we discuss and analyze the lower complexity of GCNH, which results in fewer trainable parameters and faster training times than other methods, and show how GCNH mitigates the oversmoothing problem.