mlsanityData to 7 Oct 2026

Curvature Graph Neural Network

arXiv 2106.15762 ↗First posted 30 Jun 2021cs.LG cs.AIcited by 24

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Abstract (arXiv)

Graph neural networks (GNNs) have achieved great success in many graph-based tasks. Much work is dedicated to empowering GNNs with the adaptive locality ability, which enables measuring the importance of neighboring nodes to the target node by a node-specific mechanism. However, the current node-specific mechanisms are deficient in distinguishing the importance of nodes in the topology structure. We believe that the structural importance of neighboring nodes is closely related to their importance in aggregation. In this paper, we introduce discrete graph curvature (the Ricci curvature) to quantify the strength of structural connection of pairwise nodes. And we propose Curvature Graph Neural Network (CGNN), which effectively improves the adaptive locality ability of GNNs by leveraging the structural property of graph curvature. To improve the adaptability of curvature to various datasets, we explicitly transform curvature into the weights of neighboring nodes by the necessary Negative Curvature Processing Module and Curvature Normalization Module. Then, we conduct numerous experiments on various synthetic datasets and real-world datasets. The experimental results on synthetic datasets show that CGNN effectively exploits the topology structure information, and the performance is improved significantly. CGNN outperforms the baselines on 5 dense node classification benchmark datasets. This study deepens the understanding of how to utilize advanced topology information and assign the importance of neighboring nodes from the perspective of graph curvature and encourages us to bridge the gap between graph theory and neural networks.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 41 of its 57 references that are in the map. First posted on arXiv 30 Jun 2021.

Builds on

41 of 57 references.

References · 41

  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. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,016
  6. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  7. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  8. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  9. 2016node2vec: Scalable Feature Learning for Networkscited by 1,913
  10. 2019Simplifying Graph Convolutional Networkscited by 1,470
  11. 2020Graph Contrastive Learning with Augmentationscited by 1,203
  12. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
29 more
  1. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  2. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  3. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  4. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  5. 2015Gated Graph Sequence Neural Networkscited by 792
  6. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  7. 2019Graph Neural Networks for Social Recommendationcited by 711
  8. 2019DropEdge: Towards Deep Graph Convolutional Networks on Node Classificationcited by 679
  9. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  10. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  11. 2020GCC: Graph Contrastive Coding for Graph Neural Network Pre-Trainingcited by 461
  12. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  13. 2019KGAT: Knowledge Graph Attention Network for Recommendationcited by 342
  14. 2017Community Detection and Stochastic Block Modelscited by 317
  15. 2015Improved Semantic Representations From Tree-Structured Long Short-Term Memory Networkscited by 305
  16. 2020Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networkscited by 253
  17. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  18. 2018DeepInf: Social Influence Prediction with Deep Learningcited by 128
  19. 2020When Does Self-Supervision Help Graph Convolutional Networks?cited by 121
  20. 2017Topology Adaptive Graph Convolutional Networkscited by 112
  21. 2020Self-supervised Learning on Graphs: Deep Insights and New Directioncited by 108
  22. 2019Constant Curvature Graph Convolutional Networkscited by 106
  23. 2019Community Detection on Networks with Ricci Flowcited by 62
  24. 2018Graph Transformation Policy Network for Chemical Reaction Predictioncited by 56
  25. 2019Batch Virtual Adversarial Training for Graph Convolutional Networkscited by 33
  26. 2015Ricci Curvature of the Internet Topologycited by 22
  27. 2016Characterizing Complex Networks with Forman-Ricci Curvature and Associated Geometric Flowscited by 21
  28. 2019DeepSphere: towards an equivariant graph-based spherical CNNcited by 13
  29. 2021Graph Information Vanishing Phenomenon inImplicit Graph Neural Networkscited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 3; 2025: 7; 2026: 6.

24 papers.

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  1. 2023Dynamic Graph Representation Learning with Neural Networks: A Surveycited by 15
  2. 2022Rewiring Networks for Graph Neural Network Training Using Discrete Geometrycited by 14
  3. 2022STGC-GNNs: A GNN-based traffic prediction framework with a spatial-temporal Granger causality graphcited by 12
  4. 2025Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvaturecited by 8
  5. 2023AllSpark: A Multimodal Spatio-Temporal General Intelligence Model with Ten Modalities via Language as a Reference Frameworkcited by 6
  6. 2025Enhancing Graph Representation Learning with Localized Topological Featurescited by 6
  7. 2024LSTTN: A Long-Short Term Transformer-based Spatio-temporal Neural Network for Traffic Flow Forecastingcited by 4
  8. 2026The Post-GCN Decade Revisited: Curvature-Stratified Evaluation of Relational Learningcited by 3
  9. 2023Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networkscited by 2
  10. 2024Analyzing Neural Network Robustness Using Graph Curvaturecited by 2
  11. 2025Efficient Curvature-aware Graph Networkcited by 2
  12. 2022Locally temporal-spatial pattern learning with graph attention mechanism for EEG-based emotion recognitioncited by 1
12 more
  1. 2023Graph Neural Networks with a Distribution of Parametrized Graphscited by 1
  2. 2024SeFi-CD: A Semantic First Change Detection Paradigm That Can Detect Any Change You Wantcited by 1
  3. 2026Dynamic Graph Structure Learning via Resistance Curvature Flowcited by 1
  4. 2026Geometric Flow enhanced Graph Coarseningcited by 1
  5. 2023Curvature-enhanced Graph Convolutional Network for Biomolecular Interaction Predictioncited by 0
  6. 2025Unsupervised Graph Anomaly Detection via Multi-Hypersphere Heterophilic Graph Learningcited by 0
  7. 2025Lower Ricci Curvature for Hypergraphscited by 0
  8. 2025Reconciling Attribute and Structural Anomalies for Improved Graph Anomaly Detectioncited by 0
  9. 2025A roadmap for curvature-based geometric data analysis and learningcited by 0
  10. 2026Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flowcited by 0
  11. 2026Local-Global Geometric Insights for Graph Neural Networks via Entropic Curvaturecited by 0
  12. 2026Geometric Structures on Graphs: a Holonomy-Based Discretization of Curvaturecited by 0