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Magnetic Eigenmaps for the Visualization of Directed Networks

arXiv 1606.08266 ↗First posted 27 Jun 2016cs.SI physics.soc-phcited by 25

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Abstract (arXiv)

We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jun 2016.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 4; 2024: 7; 2025: 2; 2026: 3.

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  1. 2021MagNet: A Neural Network for Directed Graphscited by 104
  2. 2023Transformers Meet Directed Graphscited by 39
  3. 2022MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplaciancited by 28
  4. 2022SigMaNet: One Laplacian to Rule Them Allcited by 23
  5. 2024Comparing Graph Transformers via Positional Encodingscited by 20
  6. 2022Geometric Scattering on Measure Spacescited by 17
  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. 2021MGC: A Complex-Valued Graph Convolutional Network for Directed Graphscited by 7
  10. 2024What Are Good Positional Encodings for Directed Graphs?cited by 7
  11. 2024HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Networkcited by 3
  12. 2024Improving Graph Neural Networks by Learning Continuous Edge Directionscited by 3
13 more
  1. 2022A Graph Convolution for Signed Directed Graphscited by 2
  2. 2023Zoo Guide to Network Embeddingcited by 2
  3. 2023Directed Scattering for Knowledge Graph-based Cellular Signaling Analysiscited by 2
  4. 2025Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approachcited by 2
  5. 2021Unraveling the graph structure of tabular data through Bayesian and spectral analysiscited by 1
  6. 2022Sparsification of the regularized magnetic Laplacian with multi-type spanning forestscited by 1
  7. 2023A Flow Artist for High-Dimensional Cellular Datacited by 1
  8. 2024A Benchmark on Directed Graph Representation Learning in Hardware Designscited by 1
  9. 2024Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphscited by 0
  10. 2025Converting Transformers into DGNNs Formcited by 0
  11. 2026Mag-Mamba: Modeling Coupled spatiotemporal Asymmetry for POI Recommendationcited by 0
  12. 2026Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representationscited by 0
  13. 2026Recovering Candidate Circadian Regulators of Arrhythmic Pituitary Hormone Genes Using Reliability-Weighted Magnetic Laplacian with rwMagLapcited by 0