mlsanityData to 7 Oct 2026

MagNet: A Neural Network for Directed Graphs

arXiv 2102.11391 ↗First posted 22 Feb 2021cs.LGcited by 104

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Abstract (arXiv)

The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets naturally modeled as directed graphs, including citation, website, and traffic networks, the vast majority of this research focuses on undirected graphs. In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian. This matrix encodes undirected geometric structure in the magnitude of its entries and directional information in their phase. A "charge" parameter attunes spectral information to variation among directed cycles. We apply our network to a variety of directed graph node classification and link prediction tasks showing that MagNet performs well on all tasks and that its performance exceeds all other methods on a majority of such tasks. The underlying principles of MagNet are such that it can be adapted to other spectral GNN architectures.

Key facts. Cited by 104 papers in the map (data through 7 Oct 2026). Builds on 28 of its 48 references that are in the map. First posted on arXiv 22 Feb 2021.

Builds on

28 of 48 references.

References · 28

  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. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,906
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,571
  8. 2013Spectral Networks and Locally Connected Networks on Graphscited by 1,097
  9. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  10. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  11. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  12. 2020Directional Message Passing for Molecular Graphscited by 556
16 more
  1. 2019Multi-scale Attributed Node Embeddingcited by 543
  2. 2017Graph Signal Processing: Overview, Challenges and Applicationscited by 409
  3. 2017Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Rankingcited by 332
  4. 2015Diffusion-Convolutional Neural Networkscited by 268
  5. 2020Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networkscited by 253
  6. 2016Higher-order organization of complex networkscited by 109
  7. 2019Transferability of Spectral Graph Convolutional Neural Networkscited by 90
  8. 2020Directed Graph Convolutional Networkcited by 73
  9. 2018MotifNet: a motif-based Graph Convolutional Network for directed graphscited by 63
  10. 2019Spectral-based Graph Convolutional Network for Directed Graphscited by 38
  11. 2020Signal Processing on Directed Graphscited by 28
  12. 2019Hermitian matrices for clustering directed graphs: insights and applicationscited by 27
  13. 2016Magnetic Eigenmaps for the Visualization of Directed Networkscited by 25
  14. 2016Magnetic eigenmaps for community detection in directed networkscited by 22
  15. 2020Characterization and comparison of large directed graphs through the spectra of the magnetic Laplaciancited by 7
  16. 2016A Note on Markov Normalized Magnetic Eigenmapscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 18; 2023: 23; 2024: 21; 2025: 18; 2026: 20.

104 papers.

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  1. 2023Edge Directionality Improves Learning on Heterophilic Graphscited by 88
  2. 2022Understanding convolution on graphs via energiescited by 58
  3. 2023A Fractional Graph Laplacian Approach to Oversmoothingcited by 45
  4. 2023Transformers Meet Directed Graphscited by 39
  5. 2022MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplaciancited by 28
  6. 2023A Survey on Spectral Graph Neural Networkscited by 26
  7. 2023Provably Powerful Graph Neural Networks for Directed Multigraphscited by 24
  8. 2022SigMaNet: One Laplacian to Rule Them Allcited by 23
  9. 2022Transformers over Directed Acyclic Graphscited by 23
  10. 2022Graph Neural Networks Designed for Different Graph Types: A Surveycited by 21
  11. 2023HoloNets: Spectral Convolutions do extend to Directed Graphscited by 20
  12. 2022Improving Graph Neural Networks with Learnable Propagation Operatorscited by 19
38 more
  1. 2023Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classificationcited by 19
  2. 2022PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphscited by 18
  3. 2022Geometric Scattering on Measure Spacescited by 17
  4. 2024Spatio-Spectral Graph Neural Networkscited by 17
  5. 2021DIGRAC: Digraph Clustering Based on Flow Imbalancecited by 15
  6. 2022A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphscited by 11
  7. 2024LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learningcited by 11
  8. 2022Signed Graph Neural Networks: A Frequency Perspectivecited by 10
  9. 2022DGEKT: A Dual Graph Ensemble Learning Method for Knowledge Tracingcited by 9
  10. 2023Dirac signal processing of higher-order topological signalscited by 9
  11. 2023Best Practices for 2-Body Pose Forecastingcited by 8
  12. 2023Graph Neural Networks based Log Anomaly Detection and Explanationcited by 8
  13. 2021MGC: A Complex-Valued Graph Convolutional Network for Directed Graphscited by 7
  14. 2022A Simple Yet Effective SVD-GCN for Directed Graphscited by 7
  15. 2023Learning Dynamic Graph Embeddings with Neural Controlled Differential Equationscited by 7
  16. 2024DUPLEX: Dual GAT for Complex Embedding of Directed Graphscited by 7
  17. 2024What Are Good Positional Encodings for Directed Graphs?cited by 7
  18. 2024GALLa: Graph Aligned Large Language Models for Improved Source Code Understandingcited by 7
  19. 2025Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embeddingcited by 7
  20. 2022Recommending Related Products Using Graph Neural Networks in Directed Graphscited by 6
  21. 2024Preventing Representational Rank Collapse in MPNNs by Splitting the Computational Graphcited by 6
  22. 2024Commute Graph Neural Networkscited by 5
  23. 2024Higher-Order Topological Directionality and Directed Simplicial Neural Networkscited by 5
  24. 2022Skew-Symmetric Adjacency Matrices for Clustering Directed Graphscited by 4
  25. 2023Signed Directed Graph Contrastive Learning with Laplacian Augmentationcited by 4
  26. 2023Improving Graph Neural Networks on Multi-node Tasks with the Labeling Trickcited by 4
  27. 2023Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNscited by 4
  28. 2023Structural Balance and Random Walks on Complex Networks with Complex Weightscited by 3
  29. 2024HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Networkcited by 3
  30. 2024DiRW: Path-Aware Digraph Learning for Heterophilycited by 3
  31. 2024Improving Graph Neural Networks by Learning Continuous Edge Directionscited by 3
  32. 2025Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scanscited by 3
  33. 2022A Graph Convolution for Signed Directed Graphscited by 2
  34. 2023Zoo Guide to Network Embeddingcited by 2
  35. 2023Directed Scattering for Knowledge Graph-based Cellular Signaling Analysiscited by 2
  36. 2024Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariancecited by 2
  37. 2024Towards Data-centric Machine Learning on Directed Graphs: a Surveycited by 2
  38. 2025Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approachcited by 2

50 most cited of 104 All 104 (JSON)