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MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing

arXiv 1905.00067 ↗First posted 30 Apr 2019cs.LG cs.SI stat.MLcited by 442

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Abstract (arXiv)

Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.

Key facts. Cited by 442 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Apr 2019.

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Citing papers per year: 2021: 77; 2022: 87; 2023: 87; 2024: 91; 2025: 70; 2026: 30.

442 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. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
  3. 2021A Survey on Deep Semi-supervised Learningcited by 250
  4. 2023Language is All a Graph Needscited by 219
  5. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  6. 2023NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classificationcited by 207
  7. 2021Is Homophily a Necessity for Graph Neural Networks?cited by 182
  8. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  9. 2021Are we really making much progress? Revisiting, benchmarking, and refining heterogeneous graph neural networkscited by 176
  10. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  11. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  12. 2023On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topologycited by 163
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  1. 2021From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awarenesscited by 154
  2. 2021Nested Graph Neural Networkscited by 136
  3. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  4. 2022Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecastingcited by 122
  5. 2022Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecastingcited by 117
  6. 2022How to Find Your Friendly Neighborhood: Graph Attention Design with Self-Supervisioncited by 102
  7. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  8. 2022Decoupling the Depth and Scope of Graph Neural Networkscited by 94
  9. 2022How Powerful are K-hop Message Passing Graph Neural Networkscited by 90
  10. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  11. 2021Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Datacited by 86
  12. 2021GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophilycited by 84
  13. 2024Graph Mamba: Towards Learning on Graphs with State Space Modelscited by 84
  14. 2021Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?cited by 82
  15. 2021New Benchmarks for Learning on Non-Homophilous Graphscited by 81
  16. 2023DRew: Dynamically Rewired Message Passing with Delaycited by 81
  17. 2021Graph-based Semi-supervised Learning: A Comprehensive Reviewcited by 79
  18. 2021Graph Representation Learning in Biomedicinecited by 79
  19. 2023Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothingcited by 67
  20. 2023Energy-based Out-of-Distribution Detection for Graph Neural Networkscited by 67
  21. 2021Reconstruction for Powerful Graph Representationscited by 65
  22. 2022Sheaf Neural Networks with Connection Laplacianscited by 64
  23. 2023Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modelingcited by 63
  24. 2021Learning Skeletal Graph Neural Networks for Hard 3D Pose Estimationcited by 62
  25. 2021On the Unreasonable Effectiveness of Feature propagation in Learning on Graphs with Missing Node Featurescited by 62
  26. 2022Structural Entropy Guided Graph Hierarchical Poolingcited by 62
  27. 2022Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyondcited by 60
  28. 2022Ordered Subgraph Aggregation Networkscited by 57
  29. 2021Simplifying approach to Node Classification in Graph Neural Networkscited by 56
  30. 2022Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNscited by 55
  31. 2023Locality-Aware Graph-Rewiring in GNNscited by 55
  32. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  33. 2021Local Augmentation for Graph Neural Networkscited by 52
  34. 2022KerGNNs: Interpretable Graph Neural Networks with Graph Kernelscited by 50
  35. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  36. 2021Search to aggregate neighborhood for graph neural networkcited by 48
  37. 2022Shortest Path Networks for Graph Property Predictioncited by 46
  38. 2021Accelerating Large Scale Real-Time GNN Inference using Channel Pruningcited by 41

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