# Simplified Graph Convolution with Heterophily

arXiv: https://arxiv.org/abs/2202.04139 · HTML: https://mlsanity.com/paper/2202.04139/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [FastGCN: Fast Learning with Graph Convolutional Networks via Importance Sampling](https://mlsanity.com/paper/1801.10247/) (2018)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Contextual Stochastic Block Models](https://mlsanity.com/paper/1807.09596/) (2018)
- [Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patterns](https://mlsanity.com/paper/2106.06586/) (2021)
- [Non-Local Graph Neural Networks](https://mlsanity.com/paper/2005.14612/) (2020)
- [Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?](https://mlsanity.com/paper/2109.05641/) (2021)
- [Minimizing Polarization and Disagreement in Social Networks](https://mlsanity.com/paper/1712.09948/) (2017)
- [Graph Frequency Analysis of Brain Signals](https://mlsanity.com/paper/1512.00037/) (2015)
- [Semi-Supervised Learning with Heterophily](https://mlsanity.com/paper/1412.3100/) (2014)

## Built on by (most cited first, 17 of 17)

- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Graph Neural Convection-Diffusion with Heterophily](https://mlsanity.com/paper/2305.16780/) (2023)
- [Towards Deep Attention in Graph Neural Networks: Problems and Remedies](https://mlsanity.com/paper/2306.02376/) (2023)
- [How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing](https://mlsanity.com/paper/2405.12474/) (2024)
- [LSGNN: Towards General Graph Neural Network in Node Classification by Local Similarity](https://mlsanity.com/paper/2305.04225/) (2023)
- [Joint Graph Rewiring and Feature Denoising via Spectral Resonance](https://mlsanity.com/paper/2408.07191/) (2024)
- [Balanced Multi-Relational Graph Clustering](https://mlsanity.com/paper/2407.16863/) (2024)
- [Incorporating Heterophily into Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2203.07678/) (2022)
- [Graph Learning and Its Advancements on Large Language Models: A Holistic Survey](https://mlsanity.com/paper/2212.08966/) (2022)
- [Diffusion-Jump GNNs: Homophiliation via Learnable Metric Filters](https://mlsanity.com/paper/2306.16976/) (2023)
- [You do not have to train Graph Neural Networks at all on text-attributed graphs](https://mlsanity.com/paper/2404.11019/) (2024)
- [Structure-Aware Group Discrimination with Adaptive-View Graph Encoder: A Fast Graph Contrastive Learning Framework](https://mlsanity.com/paper/2303.05231/) (2023)
- [Simple GNNs with Low Rank Non-parametric Aggregators](https://mlsanity.com/paper/2310.05250/) (2023)
- [SiMilarity-Enhanced Homophily for Multi-View Heterophilous Graph Clustering](https://mlsanity.com/paper/2410.03596/) (2024)
- [An Effective Universal Polynomial Basis for Spectral Graph Neural Networks](https://mlsanity.com/paper/2311.18177/) (2023)
- [Characterizing the Influence of Topology on Graph Learning Tasks](https://mlsanity.com/paper/2404.07493/) (2024)
- [Interpretable and Adaptive Node Classification on Heterophilic Graphs via Combinatorial Scoring and Hybrid Learning](https://mlsanity.com/paper/2512.22221/) (2025)

## Abstract (arXiv)

Recent work has shown that a simple, fast method called Simple Graph Convolution (SGC) (Wu et al., 2019), which eschews deep learning, is competitive with deep methods like graph convolutional networks (GCNs) (Kipf & Welling, 2017) in common graph machine learning benchmarks. The use of graph data in SGC implicitly assumes the common but not universal graph characteristic of homophily, wherein nodes link to nodes which are similar. Here we confirm that SGC is indeed ineffective for heterophilous (i.e., non-homophilous) graphs via experiments on synthetic and real-world datasets. We propose Adaptive Simple Graph Convolution (ASGC), which we show can adapt to both homophilous and heterophilous graph structure. Like SGC, ASGC is not a deep model, and hence is fast, scalable, and interpretable; further, we can prove performance guarantees on natural synthetic data models. Empirically, ASGC is often competitive with recent deep models at node classification on a benchmark of real-world datasets. The SGC paper questioned whether the complexity of graph neural networks is warranted for common graph problems involving homophilous networks; our results similarly suggest that, while deep learning often achieves the highest performance, heterophilous structure alone does not necessitate these more involved methods.