# MagNet: A Neural Network for Directed Graphs

arXiv: https://arxiv.org/abs/2102.11391 · HTML: https://mlsanity.com/paper/2102.11391/

## Key facts

- Cited by 107 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 48 references that are in the map.
- First posted on arXiv 22 Feb 2021.

## Builds on (most cited first, 28 of 28)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Multi-scale Attributed Node Embedding](https://mlsanity.com/paper/1909.13021/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Transferability of Spectral Graph Convolutional Neural Networks](https://mlsanity.com/paper/1907.12972/) (2019)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Signal Processing on Directed Graphs](https://mlsanity.com/paper/2008.00586/) (2020)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [Magnetic Eigenmaps for the Visualization of Directed Networks](https://mlsanity.com/paper/1606.08266/) (2016)
- [Magnetic eigenmaps for community detection in directed networks](https://mlsanity.com/paper/1606.07359/) (2016)
- [Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian](https://mlsanity.com/paper/2007.03466/) (2020)
- [A Note on Markov Normalized Magnetic Eigenmaps](https://mlsanity.com/paper/1608.04418/) (2016)

## Built on by (most cited first, 30 of 107)

- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [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)
- [Provably Powerful Graph Neural Networks for Directed Multigraphs](https://mlsanity.com/paper/2306.11586/) (2023)
- [A Survey on Spectral Graph Neural Networks](https://mlsanity.com/paper/2302.05631/) (2023)
- [SigMaNet: One Laplacian to Rule Them All](https://mlsanity.com/paper/2205.13459/) (2022)
- [Transformers over Directed Acyclic Graphs](https://mlsanity.com/paper/2210.13148/) (2022)
- [Graph Neural Networks Designed for Different Graph Types: A Survey](https://mlsanity.com/paper/2204.03080/) (2022)
- [HoloNets: Spectral Convolutions do extend to Directed Graphs](https://mlsanity.com/paper/2310.02232/) (2023)
- [Improving Graph Neural Networks with Learnable Propagation Operators](https://mlsanity.com/paper/2210.17224/) (2022)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Spatio-Spectral Graph Neural Networks](https://mlsanity.com/paper/2405.19121/) (2024)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs](https://mlsanity.com/paper/2210.10993/) (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)
- [DGEKT: A Dual Graph Ensemble Learning Method for Knowledge Tracing](https://mlsanity.com/paper/2211.12881/) (2022)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Best Practices for 2-Body Pose Forecasting](https://mlsanity.com/paper/2304.05758/) (2023)
- [Graph Neural Networks based Log Anomaly Detection and Explanation](https://mlsanity.com/paper/2307.00527/) (2023)
- [What Are Good Positional Encodings for Directed Graphs?](https://mlsanity.com/paper/2407.20912/) (2024)
- [Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding](https://mlsanity.com/paper/2503.18010/) (2025)
- [MGC: A Complex-Valued Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/2110.07570/) (2021)
- [A Simple Yet Effective SVD-GCN for Directed Graphs](https://mlsanity.com/paper/2205.09335/) (2022)
- [Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations](https://mlsanity.com/paper/2302.11354/) (2023)
- [DUPLEX: Dual GAT for Complex Embedding of Directed Graphs](https://mlsanity.com/paper/2406.05391/) (2024)

## 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.