mlsanityData to 7 Oct 2026

Graph Neural Networks: Architectures, Stability and Transferability

arXiv 2008.01767 ↗First posted 4 Aug 2020cs.LG stat.MLcited by 79

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Abstract (arXiv)

Graph Neural Networks (GNNs) are information processing architectures for signals supported on graphs. They are presented here as generalizations of convolutional neural networks (CNNs) in which individual layers contain banks of graph convolutional filters instead of banks of classical convolutional filters. Otherwise, GNNs operate as CNNs. Filters are composed with pointwise nonlinearities and stacked in layers. It is shown that GNN architectures exhibit equivariance to permutation and stability to graph deformations. These properties help explain the good performance of GNNs that can be observed empirically. It is also shown that if graphs converge to a limit object, a graphon, GNNs converge to a corresponding limit object, a graphon neural network. This convergence justifies the transferability of GNNs across networks with different number of nodes. Concepts are illustrated by the application of GNNs to recommendation systems, decentralized collaborative control, and wireless communication networks.

Key facts. Cited by 79 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Aug 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 13; 2022: 18; 2023: 12; 2024: 13; 2025: 12; 2026: 10.

79 papers.

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  1. 2022Equivariant and Stable Positional Encoding for More Powerful Graph Neural Networkscited by 94
  2. 2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 88
  3. 2022Theory of Graph Neural Networks: Representation and Learningcited by 60
  4. 2022Generalization Analysis of Message Passing Neural Networks on Large Random Graphscited by 58
  5. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  6. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 51
  7. 2021How Powerful is Graph Convolution for Recommendation?cited by 50
  8. 2022OOD Link Prediction Generalization Capabilities of Message-Passing GNNs in Larger Test Graphscited by 38
  9. 2023Convolutional Learning on Simplicial Complexescited by 26
  10. 2021Graph-based Deep Learning for Communication Networks: A Surveycited by 21
  11. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  12. 2022coVariance Neural Networkscited by 18
38 more
  1. 2024Generalization Bounds for Message Passing Networks on Mixture of Graphonscited by 16
  2. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  3. 2021Graph Neural Networks for Decentralized Multi-Robot Submodular Action Selectioncited by 13
  4. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  5. 2022From Local to Global: Spectral-Inspired Graph Neural Networkscited by 11
  6. 2022Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysiscited by 10
  7. 2021ModGNN: Expert Policy Approximation in Multi-Agent Systems with a Modular Graph Neural Network Architecturecited by 9
  8. 2021Intelligent Zero Trust Architecture for 5G/6G Networks: Principles, Challenges, and the Role of Machine Learning in the context of O-RANcited by 9
  9. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  10. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  11. 2022Convergence of Invariant Graph Networkscited by 8
  12. 2023Unsupervised Learning of Sampling Distributions for Particle Filterscited by 8
  13. 2024Redesigning graph filter-based GNNs to relax the homophily assumptioncited by 8
  14. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  15. 2021Scalable Perception-Action-Communication Loops with Convolutional and Graph Neural Networkscited by 7
  16. 2021A Computational Framework for Modeling Complex Sensor Network Data Using Graph Signal Processing and Graph Neural Networks in Structural Health Monitoringcited by 6
  17. 2024Convolutional Learning on Directed Acyclic Graphscited by 6
  18. 2024Sparse Covariance Neural Networkscited by 6
  19. 2025Generative Diffusion Models for Resource Allocation in Wireless Networkscited by 6
  20. 2022A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphscited by 5
  21. 2024Graph neural networks and non-commuting operatorscited by 5
  22. 2025Graph Signal Generative Diffusion Modelscited by 5
  23. 2022Predicting Brain Age using Transferable coVariance Neural Networkscited by 4
  24. 2024Survey of Graph Neural Network for Internet of Things and NextG Networkscited by 4
  25. 2023Graph Neural Networks for Decentralized Multi-Agent Perimeter Defensecited by 3
  26. 2023Framelet Message Passingcited by 3
  27. 2023Learning to Navigate in Turbulent Flows with Aerial Robot Swarms: A Cooperative Deep Reinforcement Learning Approachcited by 3
  28. 2023Robust Graph Neural Network based on Graph Denoisingcited by 3
  29. 2024LPAC: Learnable Perception-Action-Communication Loops with Applications to Coverage Controlcited by 3
  30. 2025Covariance Density Neural Networkscited by 3
  31. 2021Stability Analysis of Unfolded WMMSE for Power Allocationcited by 2
  32. 2022Interpretable and Effective Reinforcement Learning for Attacking against Graph-based Rumor Detectioncited by 2
  33. 2022Towards Understanding Graph Neural Networks: An Algorithm Unrolling Perspectivecited by 2
  34. 2022Learning Decentralized Strategies for a Perimeter Defense Game with Graph Neural Networkscited by 2
  35. 2022Stable and Transferable Hyper-Graph Neural Networkscited by 2
  36. 2023Graph Neural Networks over the Air for Decentralized Tasks in Wireless Networkscited by 2
  37. 2023Robust Angular Synchronization via Directed Graph Neural Networkscited by 2
  38. 2023A Local Graph Limits Perspective on Sampling-Based GNNscited by 2

50 most cited of 79 All 79 (JSON)