MagNet: A Neural Network for Directed Graphs

2021/02/22 by Xitong Zhang, Yixuan He, Zhang, Xitong +7 · 9 citations
Computer Science · Physics and Astronomy · #Advanced Graph Neural Networks #Complex Network Analysis Techniques #FOS: Computer and information sciences #Graph Theory and Algorithms #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2102.11391

openalex publication_date 2021/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

, a 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 GNN architectures.

Citations

• Laplacians and the Cheeger Inequality for Directed Graphs
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Inductive Representation Learning on Large Graphs
• Graph Neural Networks: A Review of Methods and Applications
• Detecting Functionality-Specific Vulnerabilities via Retrieving Individual Functionality-Equivalent APIs in Open-Source Repositories
• Directed Graph Convolutional Network
• Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks
• A Comprehensive Survey on Graph Neural Networks

Cited by

• Gauge-Equivariant Graph Networks via Self-Interference Cancellation
• Complex-Weighted Convolutional Networks: Provable Expressiveness via Complex Diffusion
• Toward General Digraph Contrastive Learning: A Dual Spatial Perspective
• Capturing Intransitive Dominance in Tennis Forecasting: A Graph Neural Network Approach
• Structured Spectral Graph Representation Learning for Multi-label Abnormality Analysis from 3D CT Scans
• SVD-Based UGRM-GFT on Directed Product Graphs
• Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs
• State Space Models over Directed Graphs
• Flow Matters: Directional and Expressive GNNs for Heterophilic Graphs

Related

• MGC: A Complex-Valued Graph Convolutional Network for Directed Graphs
• MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian
• A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs
• LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning
• HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network