mlsanityData to 7 Oct 2026

Graph Neural Convection-Diffusion with Heterophily

arXiv 2305.16780 ↗First posted 26 May 2023cs.LG cs.SIcited by 26

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Abstract (arXiv)

Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at urlhttps://github.com/zknus/Graph-Diffusion-CDE.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 33 of its 61 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

33 of 61 references.

References · 33

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  4. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  5. 2017Graph Attention Networkscited by 8,854
  6. 2017Inductive Representation Learning on Large Graphscited by 6,284
  7. 2018How Powerful are Graph Neural Networks?cited by 4,355
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2016Variational Graph Auto-Encoderscited by 1,373
  10. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  11. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  12. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
21 more
  1. 2019Multi-scale Attributed Node Embeddingcited by 543
  2. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  3. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 332
  4. 2021GRAND: Graph Neural Diffusioncited by 258
  5. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  6. 2020Graph Neural Networks with Heterophilycited by 202
  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. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  10. 2022Graph-Coupled Oscillator Networkscited by 123
  11. 2021Stable Neural ODE with Lyapunov-Stable Equilibrium Points for Defending Against Adversarial Attackscited by 91
  12. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  13. 2021GBK-GNN: Gated Bi-Kernel Graph Neural Networks for Modeling Both Homophily and Heterophilycited by 84
  14. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  15. 2022On the Robustness of Graph Neural Diffusion to Topology Perturbationscited by 30
  16. 2021How does Heterophily Impact the Robustness of Graph Neural Networks? Theoretical Connections and Practical Implicationscited by 21
  17. 2022RobustLoc: Robust Camera Pose Regression in Challenging Driving Environmentscited by 18
  18. 2022Simplified Graph Convolution with Heterophilycited by 17
  19. 2022SGAT: Simplicial Graph Attention Networkcited by 16
  20. 2019Error-Correcting Output Codes with Ensemble Diversity for Robust Learning in Neural Networkscited by 11
  21. 2023Leveraging Label Non-Uniformity for Node Classification in Graph Neural Networkscited by 11

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 9; 2025: 8; 2026: 3.

26 papers.

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  1. 2023From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyondcited by 26
  2. 2023Adversarial Robustness in Graph Neural Networks: A Hamiltonian Approachcited by 24
  3. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  4. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  5. 2023Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networkscited by 12
  6. 2024Coupling Graph Neural Networks with Fractional Order Continuous Dynamics: A Robustness Studycited by 9
  7. 2024On The Temporal Domain of Differential Equation Inspired Graph Neural Networkscited by 9
  8. 2025Message-Passing State-Space Models: Improving Graph Learning with Modern Sequence Modelingcited by 9
  9. 2023Supercharging Graph Transformers with Advective Diffusioncited by 7
  10. 2024Distributed-Order Fractional Graph Operating Networkcited by 7
  11. 2025Neural Variable-Order Fractional Differential Equation Networkscited by 5
  12. 2024Improving Graph Neural Networks by Learning Continuous Edge Directionscited by 3
14 more
  1. 2024Quadratic Binary Optimization with Graph Neural Networkscited by 2
  2. 2023Graph Neural Networks with a Distribution of Parametrized Graphscited by 1
  3. 2023Resilient Graph Neural Networks: A Coupled Dynamical Systems Approachcited by 1
  4. 2024Link Prediction with Physics-Inspired Graph Neural Networkscited by 1
  5. 2024HyperAggregation: Aggregating over Graph Edges with Hypernetworkscited by 1
  6. 2024Dirac--Bianconi Graph Neural Networks -- Enabling Non-Diffusive Long-Range Graph Predictionscited by 1
  7. 2025Resolving Oversmoothing with Opinion Dissensuscited by 1
  8. 2025Hierarchical Uncertainty-Aware Graph Neural Networkcited by 1
  9. 2025Graph Neural Diffusion via Generalized Opinion Dynamicscited by 1
  10. 2025Simple Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  11. 2025Adaptive Multi-view Graph Contrastive Learning via Fractional-order Neural Diffusion Networkscited by 0
  12. 2026Neighbourhood Transformer: Switchable Attention for Monophily-Aware Graph Learningcited by 0
  13. 2026Graph Navier Stokes Networkscited by 0
  14. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0