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A Survey on Spectral Graph Neural Networks

arXiv 2302.05631 ↗First posted 11 Feb 2023cs.LG cs.AI cs.SIcited by 26

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Abstract (arXiv)

Graph neural networks (GNNs) have attracted considerable attention from the research community. It is well established that GNNs are usually roughly divided into spatial and spectral methods. Despite that spectral GNNs play an important role in both graph signal processing and graph representation learning, existing studies are biased toward spatial approaches, and there is no comprehensive review on spectral GNNs so far. In this paper, we summarize the recent development of spectral GNNs, including model, theory, and application. Specifically, we first discuss the connection between spatial GNNs and spectral GNNs, which shows that spectral GNNs can capture global information and have better expressiveness and interpretability. Next, we categorize existing spectral GNNs according to the spectrum information they use, ie, eigenvalues or eigenvectors. In addition, we review major theoretical results and applications of spectral GNNs, followed by a quantitative experiment to benchmark some popular spectral GNNs. Finally, we conclude the paper with some future directions.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). Builds on 51 of its 63 references that are in the map. First posted on arXiv 11 Feb 2023.

Builds on

51 of 63 references.

References · 51

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38 more
  1. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 993
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Citing papers per year: 2023: 4; 2024: 13; 2025: 9.

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  1. 2023Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphscited by 39
  2. 2024Graph Transformers: A Surveycited by 32
  3. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  4. 2024Graph Condensation: A Surveycited by 23
  5. 2023Graph Neural Network-based EEG Classification: A Surveycited by 21
  6. 2024Spectral Invariant Learning for Dynamic Graphs under Distribution Shiftscited by 19
  7. 2024Spatio-Spectral Graph Neural Networkscited by 17
  8. 2024FedSSP: Federated Graph Learning with Spectral Knowledge and Personalized Preferencecited by 16
  9. 2023Exploring Causal Learning through Graph Neural Networks: An In-depth Reviewcited by 8
  10. 2024Beyond Sequence: Impact of Geometric Context for RNA Property Predictioncited by 8
  11. 2023Shape-aware Graph Spectral Learningcited by 6
  12. 2024Graph Fourier Neural Kernels (G-FuNK): Learning Solutions of Nonlinear Diffusive Parametric PDEs on Multiple Domainscited by 5
14 more
  1. 2024ERGNN: Spectral Graph Neural Network With Explicitly-Optimized Rational Graph Filterscited by 5
  2. 2024Beyond Grid Data: Exploring Graph Neural Networks for Earth Observationcited by 3
  3. 2024Graph Neural Networks Are More Than Filters: Revisiting and Benchmarking from A Spectral Perspectivecited by 3
  4. 2025Graph Persistence goes Spectralcited by 2
  5. 2025Learnable quantum spectral filters for hybrid graph neural networkscited by 1
  6. 2024Coefficient Decomposition for Spectral Graph Convolutioncited by 0
  7. 2024YOSO: You-Only-Sample-Once via Compressed Sensing for Graph Neural Network Trainingcited by 0
  8. 2025Rethinking Link Prediction for Directed Graphscited by 0
  9. 2025Interpretable graph-based models on multimodal biomedical data integration: A technical review and benchmarkingcited by 0
  10. 2025Spectral Manifold Harmonization for Graph Imbalanced Regressioncited by 0
  11. 2025A Graph Laplacian Eigenvector-based Pre-training Method for Graph Neural Networkscited by 0
  12. 2025Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edgescited by 0
  13. 2025Grassmanian Interpolation of Low-Pass Graph Filters: Theory and Applicationscited by 0
  14. 2025Multi-Head Spectral-Adaptive Graph Anomaly Detectioncited by 0