mlsanityData to 7 Oct 2026

Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs

arXiv 2306.07608 ↗First posted 13 Jun 2023cs.SI cs.AIcited by 25

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Abstract (arXiv)

Real-world graphs generally have only one kind of tendency in their connections. These connections are either homophily-prone or heterophily-prone. While graphs with homophily-prone edges tend to connect nodes with the same class (i.e., intra-class nodes), heterophily-prone edges tend to build relationships between nodes with different classes (i.e., inter-class nodes). Existing GNNs only take the original graph during training. The problem with this approach is that it forgets to take into consideration the ``missing-half" structural information, that is, heterophily-prone topology for homophily-prone graphs and homophily-prone topology for heterophily-prone graphs. In our paper, we introduce Graph cOmplementAry Learning, namely GOAL, which consists of two components: graph complementation and complemented graph convolution. The first component finds the missing-half structural information for a given graph to complement it. The complemented graph has two sets of graphs including both homophily- and heterophily-prone topology. In the latter component, to handle complemented graphs, we design a new graph convolution from the perspective of optimisation. The experiment results show that GOAL consistently outperforms all baselines in eight real-world datasets.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). Builds on 36 of its 48 references that are in the map. First posted on arXiv 13 Jun 2023.

Builds on

36 of 48 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. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  6. 2019Simplifying Graph Convolutional Networkscited by 1,470
  7. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  8. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  9. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  10. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  11. 2020Simple and Deep Graph Convolutional Networkscited by 857
  12. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
24 more
  1. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  2. 2019Multi-scale Attributed Node Embeddingcited by 543
  3. 2019Diffusion Improves Graph Learningcited by 414
  4. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  5. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  6. 2021Interpreting and Unifying Graph Neural Networks with An Optimization Frameworkcited by 131
  7. 2021Deep Graph Clustering via Dual Correlation Reductioncited by 97
  8. 2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 88
  9. 2022Federated Learning on Non-IID Graphs via Structural Knowledge Sharingcited by 88
  10. 2022Multivariate Time Series Forecasting with Dynamic Graph Neural ODEscited by 72
  11. 2022Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discriminationcited by 67
  12. 2020Tackling Over-Smoothing for General Graph Convolutional Networkscited by 66
  13. 2022Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminatingcited by 57
  14. 2022GOOD-D: On Unsupervised Graph Out-Of-Distribution Detectioncited by 47
  15. 2021Pseudo-Riemannian Graph Convolutional Networkscited by 30
  16. 2020Bridging the Gap Between Spectral and Spatial Domains in Graph Neural Networkscited by 26
  17. 2022Spiking Graph Convolutional Networkscited by 26
  18. 2023Auto-HeG: Automated Graph Neural Network on Heterophilic Graphscited by 23
  19. 2023Normalizing Flow-based Neural Process for Few-Shot Knowledge Graph Completioncited by 19
  20. 2023Unraveling Privacy Risks of Individual Fairness in Graph Neural Networkscited by 16
  21. 2021Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filteringcited by 14
  22. 2022Projective Ranking-based GNN Evasion Attackscited by 14
  23. 2022Unifying Graph Contrastive Learning with Flexible Contextual Scopescited by 14
  24. 2022Graph Sequential Neural ODE Process for Link Prediction on Dynamic and Sparse Graphscited by 13

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 8; 2024: 8; 2025: 7; 2026: 2.

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  1. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  2. 2024ARC: A Generalist Graph Anomaly Detector with In-Context Learningcited by 46
  3. 2023Towards Self-Interpretable Graph-Level Anomaly Detectioncited by 41
  4. 2024Large Language Models-guided Dynamic Adaptation for Temporal Knowledge Graph Reasoningcited by 41
  5. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
  6. 2023PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detectioncited by 25
  7. 2025A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detectioncited by 24
  8. 2023GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labelscited by 17
  9. 2024GOODAT: Towards Test-time Graph Out-of-Distribution Detectioncited by 17
  10. 2024Self-Supervision Improves Diffusion Models for Tabular Data Imputationcited by 16
  11. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  12. 2024Understanding Heterophily for Graph Neural Networkscited by 15
13 more
  1. 2024Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformationcited by 15
  2. 2024Sign is Not a Remedy: Multiset-to-Multiset Message Passing for Learning on Heterophilic Graphscited by 8
  3. 2023Mixture of Weak & Strong Experts on Graphscited by 7
  4. 2025Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophilycited by 5
  5. 2023Refining Latent Homophilic Structures over Heterophilic Graphs for Robust Graph Convolution Networkscited by 4
  6. 2024RIDA: A Robust Attack Framework on Incomplete Graphscited by 1
  7. 2025FedHERO: A Federated Learning Approach for Node Classification Task on Heterophilic Graphscited by 1
  8. 2025Does Homophily Help in Robust Test-time Node Classification?cited by 1
  9. 2025A Generative Graph Contrastive Learning Model with Global Signalcited by 0
  10. 2025GraphTorque: Torque-Driven Rewiring Graph Neural Networkcited by 0
  11. 2025Adaptive Graph Mixture of Residual Experts: Unsupervised Learning on Diverse Graphs with Heterogeneous Specializationcited by 0
  12. 2026Invariant-Stratified Propagation for Expressive Graph Neural Networkscited by 0
  13. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0