# Magnetic Eigenmaps for the Visualization of Directed Networks

arXiv: https://arxiv.org/abs/1606.08266 · HTML: https://mlsanity.com/paper/1606.08266/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2016.

## Built on by (most cited first, 25 of 25)

- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Transformers Meet Directed Graphs](https://mlsanity.com/paper/2302.00049/) (2023)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [SigMaNet: One Laplacian to Rule Them All](https://mlsanity.com/paper/2205.13459/) (2022)
- [Comparing Graph Transformers via Positional Encodings](https://mlsanity.com/paper/2402.14202/) (2024)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning](https://mlsanity.com/paper/2401.11772/) (2024)
- [Signed Graph Neural Networks: A Frequency Perspective](https://mlsanity.com/paper/2208.07323/) (2022)
- [What Are Good Positional Encodings for Directed Graphs?](https://mlsanity.com/paper/2407.20912/) (2024)
- [MGC: A Complex-Valued Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/2110.07570/) (2021)
- [HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network](https://mlsanity.com/paper/2402.09676/) (2024)
- [Improving Graph Neural Networks by Learning Continuous Edge Directions](https://mlsanity.com/paper/2410.14109/) (2024)
- [A Graph Convolution for Signed Directed Graphs](https://mlsanity.com/paper/2208.11511/) (2022)
- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Directed Scattering for Knowledge Graph-based Cellular Signaling Analysis](https://mlsanity.com/paper/2309.07813/) (2023)
- [Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach](https://mlsanity.com/paper/2501.11817/) (2025)
- [Unraveling the graph structure of tabular data through Bayesian and spectral analysis](https://mlsanity.com/paper/2110.01421/) (2021)
- [Sparsification of the regularized magnetic Laplacian with multi-type spanning forests](https://mlsanity.com/paper/2208.14797/) (2022)
- [A Flow Artist for High-Dimensional Cellular Data](https://mlsanity.com/paper/2308.00176/) (2023)
- [A Benchmark on Directed Graph Representation Learning in Hardware Designs](https://mlsanity.com/paper/2410.06460/) (2024)
- [Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphs](https://mlsanity.com/paper/2406.01517/) (2024)
- [Converting Transformers into DGNNs Form](https://mlsanity.com/paper/2502.00585/) (2025)
- [Mag-Mamba: Modeling Coupled spatiotemporal Asymmetry for POI Recommendation](https://mlsanity.com/paper/2603.00053/) (2026)
- [Complex Diffusion Maps with ω-Parameterized Kernels Revealing Inherent Harmonic Representations](https://mlsanity.com/paper/2605.01691/) (2026)
- [Recovering Candidate Circadian Regulators of Arrhythmic Pituitary Hormone Genes Using Reliability-Weighted Magnetic Laplacian with rwMagLap](https://mlsanity.com/paper/2607.06579/) (2026)

## 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.