# Spectral-based Graph Convolutional Network for Directed Graphs

arXiv: https://arxiv.org/abs/1907.08990 · HTML: https://mlsanity.com/paper/1907.08990/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2019.

## Built on by (most cited first, 30 of 38)

- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (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)
- [Transformers over Directed Acyclic Graphs](https://mlsanity.com/paper/2210.13148/) (2022)
- [Directed Graph Auto-Encoders](https://mlsanity.com/paper/2202.12449/) (2022)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [High Fidelity 3D Hand Shape Reconstruction via Scalable Graph Frequency Decomposition](https://mlsanity.com/paper/2307.05541/) (2023)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [WGCN: Graph Convolutional Networks with Weighted Structural Features](https://mlsanity.com/paper/2104.14060/) (2021)
- [A Magnetic Framelet-Based Convolutional Neural Network for Directed Graphs](https://mlsanity.com/paper/2210.10993/) (2022)
- [D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning](https://mlsanity.com/paper/2112.11734/) (2021)
- [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)
- [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)
- [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)
- [A Simple and Scalable Graph Neural Network for Large Directed Graphs](https://mlsanity.com/paper/2306.08274/) (2023)
- [Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance](https://mlsanity.com/paper/2410.16935/) (2024)
- [Towards Data-centric Machine Learning on Directed Graphs: a Survey](https://mlsanity.com/paper/2412.01849/) (2024)
- [Asymmetric Graph Representation Learning](https://mlsanity.com/paper/2110.07436/) (2021)
- [GRANDE: a neural model over directed multigraphs with application to anti-money laundering](https://mlsanity.com/paper/2302.02101/) (2023)
- [DEDGAT: Dual Embedding of Directed Graph Attention Networks for Detecting Financial Risk](https://mlsanity.com/paper/2303.03933/) (2023)
- [Can Directed Graph Neural Networks be Adversarially Robust?](https://mlsanity.com/paper/2306.02002/) (2023)
- [A Benchmark on Directed Graph Representation Learning in Hardware Designs](https://mlsanity.com/paper/2410.06460/) (2024)
- [Scale-aware Message Passing For Graph Node Classification](https://mlsanity.com/paper/2411.19392/) (2024)
- [LineMVGNN: Anti-Money Laundering with Line-Graph-Assisted Multi-View Graph Neural Networks](https://mlsanity.com/paper/2603.23584/) (2026)

## Abstract (arXiv)

Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-based GCNs have achieved impressive results in many graph related analytics tasks. However, spectral-based models cannot directly work on directed graphs. In this paper, we propose an improved spectral-based GCN for the directed graph by leveraging redefined Laplacians to improve its propagation model. Our approach can work directly on directed graph data in semi-supervised nodes classification tasks. Experiments on a number of directed graph datasets demonstrate that our approach outperforms the state-of-the-art methods.