mlsanityData to 7 Oct 2026

HoloNets: Spectral Convolutions do extend to Directed Graphs

arXiv 2310.02232 ↗First posted 3 Oct 2023cs.LG cs.SIcited by 20

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Abstract (arXiv)

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 33 of its 68 references that are in the map. First posted on arXiv 3 Oct 2023.

Builds on

33 of 68 references.

References · 33

  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. 2020Open Graph Benchmark: Datasets for Machine Learning on Graphscited by 2,148
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  6. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  7. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  8. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  9. 2023A critical look at the evaluation of GNNs under heterophily: Are we really making progress?cited by 332
  10. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
  11. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  12. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
21 more
  1. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  2. 2019Graph Neural Networks with convolutional ARMA filterscited by 185
  3. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  4. 2022How Powerful are Spectral Graph Neural Networkscited by 169
  5. 2022Revisiting Heterophily For Graph Neural Networkscited by 169
  6. 2020Directional Graph Networkscited by 132
  7. 2021MagNet: A Neural Network for Directed Graphscited by 104
  8. 2023Specformer: Spectral Graph Neural Networks Meet Transformerscited by 102
  9. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 90
  10. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  11. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  12. 2021Transferability of Graph Neural Networks: an Extended Graphon Approachcited by 51
  13. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  14. 2021Transferability Properties of Graph Neural Networkscited by 42
  15. 2021Improving Graph Neural Networks with Simple Architecture Designcited by 41
  16. 2023Transformers Meet Directed Graphscited by 39
  17. 2022MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplaciancited by 28
  18. 2023Limitless stability for Graph Convolutional Networkscited by 2
  19. 2023Graph Scattering beyond Wavelet Shacklescited by 2
  20. 2018Diffusion and consensus on weakly connected directed graphscited by 1
  21. 2023ResolvNet: A Graph Convolutional Network with multi-scale Consistencycited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 8; 2025: 8; 2026: 4.

20 papers.

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  1. 2024Spatio-Spectral Graph Neural Networkscited by 17
  2. 2024FSW-GNN: A Bi-Lipschitz WL-Equivalent Graph Neural Networkcited by 8
  3. 2024What Are Good Positional Encodings for Directed Graphs?cited by 7
  4. 2025Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embeddingcited by 7
  5. 2024Commute Graph Neural Networkscited by 5
  6. 2024Improving Graph Neural Networks by Learning Continuous Edge Directionscited by 3
  7. 2024Towards Data-centric Machine Learning on Directed Graphs: a Surveycited by 2
  8. 2025Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approachcited by 2
  9. 2024A Benchmark on Directed Graph Representation Learning in Hardware Designscited by 1
  10. 2024Scale-aware Message Passing For Graph Node Classificationcited by 1
  11. 2025Preference-driven Knowledge Distillation for Few-shot Node Classificationcited by 1
  12. 2026LineMVGNN: Anti-Money Laundering with Line-Graph-Assisted Multi-View Graph Neural Networkscited by 1
8 more
  1. 2026Nonlinear Laplacians Improve Signed-Directed Graph Learningcited by 1
  2. 2025Rethinking Link Prediction for Directed Graphscited by 0
  3. 2025Toward Data-centric Directed Graph Learning: An Entropy-driven Approachcited by 0
  4. 2025Directed Semi-Simplicial Learning with Applications to Brain Activity Decodingcited by 0
  5. 2025State Space Models over Directed Graphscited by 0
  6. 2025Training Diverse Graph Experts for Ensembles: A Systematic Empirical Studycited by 0
  7. 2026Position: Spectral GNNs Are Neither Spectral Nor Superior for Node Classificationcited by 0
  8. 2026TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networkscited by 0