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Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks

arXiv 2003.03777 ↗First posted 8 Mar 2020cs.LG cs.SY eess.SYcited by 73

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Abstract (arXiv)

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively exploit this graph structure. In this work, we leverage graph signal processing to characterize the representation space of graph neural networks (GNNs). We discuss the role of graph convolutional filters in GNNs and show that any architecture built with such filters has the fundamental properties of permutation equivariance and stability to changes in the topology. These two properties offer insight about the workings of GNNs and help explain their scalability and transferability properties which, coupled with their local and distributed nature, make GNNs powerful tools for learning in physical networks. We also introduce GNN extensions using edge-varying and autoregressive moving average graph filters and discuss their properties. Finally, we study the use of GNNs in recommender systems and learning decentralized controllers for robot swarms.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Mar 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 15; 2022: 15; 2023: 17; 2024: 7; 2025: 10; 2026: 8.

73 papers.

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  1. 2022Graph Filters for Signal Processing and Machine Learning on Graphscited by 53
  2. 2021Transferability Properties of Graph Neural Networkscited by 42
  3. 2021Simplicial Convolutional Neural Networkscited by 40
  4. 2022Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutionscited by 28
  5. 2023Convolutional Learning on Simplicial Complexescited by 26
  6. 2022Graph Neural Networks Designed for Different Graph Types: A Surveycited by 21
  7. 2023Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Backcited by 21
  8. 2023Explainable Brain Age Prediction using coVariance Neural Networkscited by 19
  9. 2023PowerFlowNet: Power Flow Approximation Using Message Passing Graph Neural Networkscited by 19
  10. 2021Stability of Graph Convolutional Neural Networks to Stochastic Perturbationscited by 18
  11. 2022coVariance Neural Networkscited by 18
  12. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 16
38 more
  1. 2021Finite Impulse Response Filters for Simplicial Complexescited by 15
  2. 2021Wide and Deep Graph Neural Network with Distributed Online Learningcited by 14
  3. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  4. 2022Unsupervised Optimal Power Flow Using Graph Neural Networkscited by 13
  5. 2020Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learningcited by 12
  6. 2022Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysiscited by 10
  7. 2023Deep Statistical Solver for Distribution System State Estimationcited by 9
  8. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  9. 2021Graph-Time Convolutional Neural Networkscited by 8
  10. 2021Stability to Deformations of Manifold Filters and Manifold Neural Networkscited by 8
  11. 2022Convolutional Filtering in Simplicial Complexescited by 8
  12. 2023Unsupervised Learning of Sampling Distributions for Particle Filterscited by 8
  13. 2023Fairness-Aware Graph Filter Designcited by 8
  14. 2024Redesigning graph filter-based GNNs to relax the homophily assumptioncited by 8
  15. 2021Node-Variant Graph Filters in Graph Neural Networkscited by 7
  16. 2021Scalable Perception-Action-Communication Loops with Convolutional and Graph Neural Networkscited by 7
  17. 2022Stability of Aggregation Graph Neural Networkscited by 7
  18. 2022A Bipartite Graph Neural Network Approach for Scalable Beamforming Optimizationcited by 7
  19. 2023Stochastic Unrolled Federated Learningcited by 6
  20. 2024Fair CoVariance Neural Networkscited by 6
  21. 2024Sparse Covariance Neural Networkscited by 6
  22. 2021Graph Neural Networks for Learning Real-Time Prices in Electricity Marketcited by 5
  23. 2021Learning to Model the Relationship Between Brain Structural and Functional Connectomescited by 5
  24. 2022Learning Stochastic Graph Neural Networks with Constrained Variancecited by 5
  25. 2022Graph filtering over expanding graphscited by 5
  26. 2022Learning Graph Structure from Convolutional Mixturescited by 5
  27. 2023Attentional Graph Neural Network Is All You Need for Robust Massive Network Localizationcited by 5
  28. 2025Graph Signal Generative Diffusion Modelscited by 5
  29. 2021Graph Neural Networks with Parallel Neighborhood Aggregations for Graph Classificationcited by 4
  30. 2022Learning Stable Graph Neural Networks via Spectral Regularizationcited by 4
  31. 2023Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Featurescited by 4
  32. 2024Towards a Foundation Model for Brain Age Prediction using coVariance Neural Networkscited by 4
  33. 2021Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approachcited by 3
  34. 2021A Robust Alternative for Graph Convolutional Neural Networks via Graph Neighborhood Filterscited by 3
  35. 2023Learning to Navigate in Turbulent Flows with Aerial Robot Swarms: A Cooperative Deep Reinforcement Learning Approachcited by 3
  36. 2024Spectral GNN via Two-dimensional (2-D) Graph Convolutioncited by 3
  37. 2025Covariance Density Neural Networkscited by 3
  38. 2021Stability Analysis of Unfolded WMMSE for Power Allocationcited by 2

50 most cited of 73 All 73 (JSON)