mlsanityData to 7 Oct 2026

Graphon Signal Processing

arXiv 2003.05030 ↗First posted 10 Mar 2020eess.SPcited by 37

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Abstract (arXiv)

Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon Fourier transform and linear shift invariant graphon filters, the graphon counterparts of the graph Fourier transform and graph filters. It is shown that for convergent sequences of graphs and associated graph signals: (i) the graph Fourier transform converges to the graphon Fourier transform when the graphon signal is bandlimited; (ii) the spectral and vertex responses of graph filters converge to the spectral and vertex responses of graphon filters with the same coefficients. These theorems imply that for graphs that belong to certain families, i.e., that are part of sequences that converge to a certain graphon, graph Fourier analysis and graph filter design have well defined limits. In turn, these facts extend applicability of graph signal processing to graphs with large number of nodes -- since signal processing pipelines designed for limit graphons can be applied to finite graphs -- and to dynamic graphs -- since we can relate the result of SP pipelines designed for different graphs from the same convergent graph sequence.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 12; 2024: 6; 2025: 4; 2026: 5.

37 papers.

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  1. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 51
  2. 2023Does Graph Distillation See Like Vision Dataset Counterpart?cited by 45
  3. 2021Transferability Properties of Graph Neural Networkscited by 42
  4. 2023A graphon-signal analysis of graph neural networkscited by 29
  5. 2023Fine-grained Expressivity of Graph Neural Networkscited by 25
  6. 2022Implicit Graphon Neural Representationcited by 18
  7. 2023Graph Neural Tangent Kernel: Convergence on Large Graphscited by 16
  8. 2022Convolutional Neural Networks on Manifolds: From Graphs and Backcited by 13
  9. 2023Fine-tuning Graph Neural Networks by Preserving Graph Generative Patternscited by 13
  10. 2022Causal Fourier Analysis on Directed Acyclic Graphs and Posetscited by 12
  11. 2022Convolutional Learning on Multigraphscited by 10
  12. 2021Stability of Neural Networks on Manifolds to Relative Perturbationscited by 9
25 more
  1. 2023Convergence of Message Passing Graph Neural Networks with Generic Aggregation On Large Random Graphscited by 9
  2. 2023Geometric Graph Filters and Neural Networks: Limit Properties and Discriminability Trade-offscited by 9
  3. 2022Graphon Pooling for Reducing Dimensionality of Signals and Convolutional Operators on Graphscited by 8
  4. 2024Learning on Large Graphs using Intersecting Communitiescited by 8
  5. 2024Scalable Implicit Graphon Learningcited by 8
  6. 2021On the Stability of Low Pass Graph Filter With a Large Number of Edge Rewirescited by 5
  7. 2022A Spectral Analysis of Graph Neural Networks on Dense and Sparse Graphscited by 5
  8. 2024Sampling and Uniqueness Sets in Graphon Signal Processingcited by 5
  9. 2023Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Featurescited by 4
  10. 2023Transferability of Graph Neural Networks using Graphon and Sampling Theoriescited by 2
  11. 2025Learning graphons from data: Random walks, transfer operators, and spectral clusteringcited by 2
  12. 2023A Poincar'e Inequality and Consistency Results for Signal Sampling on Large Graphscited by 1
  13. 2024Transferable Graphical MARL for Real-Time Estimation in Dynamic Wireless Networkscited by 1
  14. 2026DiPhon: Diffusion on Graphons for Scalable Graph Generationcited by 1
  15. 2026Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphscited by 1
  16. 2023Generalized Graphon Process: Convergence of Graph Frequencies in Stretched Cut Distancecited by 0
  17. 2023Spectral Convergence of Complexon Shift Operatorscited by 0
  18. 2024Graph data augmentation with Gromow-Wasserstein Barycenterscited by 0
  19. 2024Sampling Transferable Graph Neural Networks with Limited Graph Informationcited by 0
  20. 2025Graph Semi-Supervised Learning for Point Classification on Data Manifoldscited by 0
  21. 2025On the Convergence and Size Transferability of Continuous-depth Graph Neural Networkscited by 0
  22. 2025A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffscited by 0
  23. 2026Decentralized Learning Strategies for Estimation Error Minimization with Graph Neural Networkscited by 0
  24. 2026Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphscited by 0
  25. 2026Graph Transfer Learning via Shared Latent Geometry: Theory and Applicationscited by 0