mlsanityData to 7 Oct 2026

Is Homophily a Necessity for Graph Neural Networks?

arXiv 2106.06134 ↗First posted 11 Jun 2021cs.LG stat.MLcited by 182

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Abstract (arXiv)

Graph neural networks (GNNs) have shown great prowess in learning representations suitable for numerous graph-based machine learning tasks. When applied to semi-supervised node classification, GNNs are widely believed to work well due to the homophily assumption ("like attracts like"), and fail to generalize to heterophilous graphs where dissimilar nodes connect. Recent works design new architectures to overcome such heterophily-related limitations, citing poor baseline performance and new architecture improvements on a few heterophilous graph benchmark datasets as evidence for this notion. In our experiments, we empirically find that standard graph convolutional networks (GCNs) can actually achieve better performance than such carefully designed methods on some commonly used heterophilous graphs. This motivates us to reconsider whether homophily is truly necessary for good GNN performance. We find that this claim is not quite true, and in fact, GCNs can achieve strong performance on heterophilous graphs under certain conditions. Our work carefully characterizes these conditions, and provides supporting theoretical understanding and empirical observations. Finally, we examine existing heterophilous graphs benchmarks and reconcile how the GCN (under)performs on them based on this understanding.

Key facts. Cited by 182 papers in the map (data through 7 Oct 2026). Builds on 36 of its 54 references that are in the map. First posted on arXiv 11 Jun 2021.

Builds on

36 of 54 references.

References · 36

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  8. 2018Graph Convolutional Neural Networks for Web-Scale Recommender Systemscited by 1,133
  9. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  10. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  11. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  12. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
24 more
  1. 2020Simple and Deep Graph Convolutional Networkscited by 857
  2. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  3. 2019Graph Neural Networks for Social Recommendationcited by 711
  4. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  5. 2019Multi-scale Attributed Node Embeddingcited by 543
  6. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 442
  7. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  8. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  9. 2018Modeling polypharmacy side effects with graph convolutional networkscited by 237
  10. 2020Graph Neural Networks with Heterophilycited by 202
  11. 2020Data Augmentation for Graph Neural Networkscited by 200
  12. 2020Say No to the Discrimination: Learning Fair Graph Neural Networks with Limited Sensitive Attribute Informationcited by 168
  13. 2018Contextual Stochastic Block Modelscited by 134
  14. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  15. 2020A Unified View on Graph Neural Networks as Graph Signal Denoisingcited by 110
  16. 2016Community detection in networks: A user guidecited by 105
  17. 2017Graph Convolutional Encoders for Syntax-aware Neural Machine Translationcited by 70
  18. 2021Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalizationcited by 70
  19. 2021Improving Graph Neural Networks with Simple Architecture Designcited by 41
  20. 2020Grale: Designing Networks for Graph Learningcited by 28
  21. 2020Knowing your FATE: Friendship, Action and Temporal Explanations for User Engagement Prediction on Social Appscited by 23
  22. 2015Homophily and missing links in citation networkscited by 21
  23. 2021A Unifying Generative Model for Graph Learning Algorithms: Label Propagation, Graph Convolutions, and Combinationscited by 18
  24. 2019A Quest for Structure: Jointly Learning the Graph Structure and Semi-Supervised Classificationcited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 6; 2022: 32; 2023: 45; 2024: 58; 2025: 28; 2026: 13.

182 papers.

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  1. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 332
  2. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  3. 2024Retrieval-Augmented Generation with Graphs (GraphRAG)cited by 170
  4. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  5. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
  6. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  7. 2021GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophilycited by 84
  8. 2024Position: Graph Foundation Models are Already Herecited by 84
  9. 2024Classic GNNs are Strong Baselines: Reassessing GNNs for Node Classificationcited by 83
  10. 2024GFT: Graph Foundation Model with Transferable Tree Vocabularycited by 82
  11. 2021Subgroup Generalization and Fairness of Graph Neural Networkscited by 69
  12. 2023Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothingcited by 67
38 more
  1. 2022Understanding and Improving Graph Injection Attack by Promoting Unnoticeabilitycited by 62
  2. 2022Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyondcited by 60
  3. 2021Simplifying approach to Node Classification in Graph Neural Networkscited by 56
  4. 2022A Non-Asymptotic Analysis of Oversmoothing in Graph Neural Networkscited by 49
  5. 2023Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detectioncited by 43
  6. 2023Demystifying Structural Disparity in Graph Neural Networks: Can One Size Fit All?cited by 41
  7. 2023Simple and Asymmetric Graph Contrastive Learning without Augmentationscited by 37
  8. 2023Fast Graph Condensation with Structure-based Neural Tangent Kernelcited by 36
  9. 2022Rewiring with Positional Encodings for Graph Neural Networkscited by 35
  10. 2022FMP: Toward Fair Graph Message Passing against Topology Biascited by 35
  11. 2022Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalizationcited by 35
  12. 2024GraphEdit: Large Language Models for Graph Structure Learningcited by 33
  13. 2023OpenGSL: A Comprehensive Benchmark for Graph Structure Learningcited by 30
  14. 2024Towards Graph Foundation Models: Learning Generalities Across Graphs via Task-Treescited by 30
  15. 2023Beyond Homophily: Reconstructing Structure for Graph-agnostic Clusteringcited by 29
  16. 2023GraphPatcher: Mitigating Degree Bias for Graph Neural Networks via Test-time Augmentationcited by 29
  17. 2024Navigating Complexity: Toward Lossless Graph Condensation via Expanding Window Matchingcited by 28
  18. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  19. 2024AdaFGL: A New Paradigm for Federated Node Classification with Topology Heterogeneitycited by 25
  20. 2022Effects of Graph Convolutions in Multi-layer Networkscited by 24
  21. 2023Towards Deep Attention in Graph Neural Networks: Problems and Remediescited by 24
  22. 2022HL-Net: Heterophily Learning Network for Scene Graph Generationcited by 22
  23. 2023A Survey on Privacy in Graph Neural Networks: Attacks, Preservation, and Applicationscited by 22
  24. 2021How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implicationscited by 21
  25. 2021Noise-robust Graph Learning by Estimating and Leveraging Pairwise Interactionscited by 20
  26. 2022Understanding Non-linearity in Graph Neural Networks from the Bayesian-Inference Perspectivecited by 19
  27. 2023Permutation Equivariant Graph Framelets for Heterophilous Graph Learningcited by 19
  28. 2023A Neural Collapse Perspective on Feature Evolution in Graph Neural Networkscited by 19
  29. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  30. 2025Edge Prompt Tuning for Graph Neural Networkscited by 18
  31. 2025Towards Quantifying Long-Range Interactions in Graph Machine Learning: a Large Graph Dataset and a Measurementcited by 18
  32. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 18
  33. 2021Label-Wise Graph Convolutional Network for Heterophilic Graphscited by 17
  34. 2024Node-wise Filtering in Graph Neural Networks: A Mixture of Experts Approachcited by 17
  35. 2022Augmentation-Free Graph Contrastive Learning with Performance Guaranteecited by 16
  36. 2024Rethinking Node-wise Propagation for Large-scale Graph Learningcited by 16
  37. 2024OpenFGL: A Comprehensive Benchmark for Federated Graph Learningcited by 16
  38. 2022Exploiting Neighbor Effect: Conv-Agnostic GNNs Framework for Graphs with Heterophilycited by 15

50 most cited of 182 All 182 (JSON)