# Graph Neural Networks for Graphs with Heterophily: A Survey

arXiv: https://arxiv.org/abs/2202.07082 · HTML: https://mlsanity.com/paper/2202.07082/

## Key facts

- Cited by 175 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 168 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 30 of 58)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (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)
- [GNNExplainer: Generating Explanations for Graph Neural Networks](https://mlsanity.com/paper/1903.03894/) (2019)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Cluster-GCN: An Efficient Algorithm for Training Deep and Large Graph Convolutional Networks](https://mlsanity.com/paper/1905.07953/) (2019)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Parameterized Explainer for Graph Neural Network](https://mlsanity.com/paper/2011.04573/) (2020)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNs](https://mlsanity.com/paper/2202.04579/) (2022)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [GNNGuard: Defending Graph Neural Networks against Adversarial Attacks](https://mlsanity.com/paper/2006.08149/) (2020)
- [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)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Adversarial Attack and Defense on Graph Data: A Survey](https://mlsanity.com/paper/1812.10528/) (2018)

## Built on by (most cited first, 30 of 175)

- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [Trustworthy Graph Neural Networks: Aspects, Methods and Trends](https://mlsanity.com/paper/2205.07424/) (2022)
- [Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data](https://mlsanity.com/paper/2306.02664/) (2023)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Multi-Domain Graph Foundation Models: Robust Knowledge Transfer via Topology Alignment](https://mlsanity.com/paper/2502.02017/) (2025)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneity](https://mlsanity.com/paper/2401.11750/) (2024)
- [Class-Imbalanced Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.04300/) (2023)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [Beyond Real-world Benchmark Datasets: An Empirical Study of Node Classification with GNNs](https://mlsanity.com/paper/2206.09144/) (2022)
- [Auto-HeG: Automated Graph Neural Network on Heterophilic Graphs](https://mlsanity.com/paper/2302.12357/) (2023)
- [Graph Condensation: A Survey](https://mlsanity.com/paper/2401.11720/) (2024)
- [A Survey on Privacy in Graph Neural Networks: Attacks, Preservation, and Applications](https://mlsanity.com/paper/2308.16375/) (2023)
- [Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challenges](https://mlsanity.com/paper/2311.07073/) (2023)
- [Permutation Equivariant Graph Framelets for Heterophilous Graph Learning](https://mlsanity.com/paper/2306.04265/) (2023)
- [A Neural Collapse Perspective on Feature Evolution in Graph Neural Networks](https://mlsanity.com/paper/2307.01951/) (2023)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection](https://mlsanity.com/paper/2307.08390/) (2023)
- [Node-oriented Spectral Filtering for Graph Neural Networks](https://mlsanity.com/paper/2212.03654/) (2022)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [OpenFGL: A Comprehensive Benchmark for Federated Graph Learning](https://mlsanity.com/paper/2408.16288/) (2024)
- [Exploiting Neighbor Effect: Conv-Agnostic GNNs Framework for Graphs with Heterophily](https://mlsanity.com/paper/2203.11200/) (2022)

## Abstract (arXiv)

Recent years have witnessed fast developments of graph neural networks (GNNs) that have benefited myriad graph analytic tasks and applications. Most GNNs rely on the homophily assumption that nodes belonging to the same class are more likely to be connected. However, as a ubiquitous graph property in numerous real-world scenarios, heterophily, i.e., nodes with different labels tend to be linked, significantly limits the performance of tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining increasing research attention to enhance graph learning with heterophily. In this paper, we provide a comprehensive review of GNNs for heterophilic graphs. Specifically, we propose a systematic taxonomy that governs existing heterophilic GNN models, along with general summaries and detailed analyses. Furthermore, we discuss the relationship between heterophily and various graph research domains, aiming to facilitate the development of more effective GNNs across a spectrum of practical applications and learning tasks in the graph research community. In the end, we point out potential directions to advance and inspire future research and applications on heterophilic graph learning with GNNs.