# Directed Graph Convolutional Network

arXiv: https://arxiv.org/abs/2004.13970 · HTML: https://mlsanity.com/paper/2004.13970/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2020.

## Built on by (most cited first, 30 of 73)

- [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)
- [Space-Time-Separable Graph Convolutional Network for Pose Forecasting](https://mlsanity.com/paper/2110.04573/) (2021)
- [A Fractional Graph Laplacian Approach to Oversmoothing](https://mlsanity.com/paper/2305.13084/) (2023)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [From Continuous Dynamics to Graph Neural Networks: Neural Diffusion and Beyond](https://mlsanity.com/paper/2310.10121/) (2023)
- [SigMaNet: One Laplacian to Rule Them All](https://mlsanity.com/paper/2205.13459/) (2022)
- [Directed Graph Auto-Encoders](https://mlsanity.com/paper/2202.12449/) (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)
- [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)
- [RA-GCN: Graph Convolutional Network for Disease Prediction Problems with Imbalanced Data](https://mlsanity.com/paper/2103.00221/) (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)
- [Dynamic Dense Graph Convolutional Network for Skeleton-based Human Motion Prediction](https://mlsanity.com/paper/2311.17408/) (2023)
- [Semantic2Graph: Graph-based Multi-modal Feature Fusion for Action Segmentation in Videos](https://mlsanity.com/paper/2209.05653/) (2022)
- [D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning](https://mlsanity.com/paper/2112.11734/) (2021)
- [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)
- [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)
- [Recommending Related Products Using Graph Neural Networks in Directed Graphs](https://mlsanity.com/paper/2211.11583/) (2022)
- [Commute Graph Neural Networks](https://mlsanity.com/paper/2407.01635/) (2024)
- [Higher-Order Topological Directionality and Directed Simplicial Neural Networks](https://mlsanity.com/paper/2409.08389/) (2024)
- [Signed Directed Graph Contrastive Learning with Laplacian Augmentation](https://mlsanity.com/paper/2301.05163/) (2023)
- [Improving Graph Neural Networks on Multi-node Tasks with the Labeling Trick](https://mlsanity.com/paper/2304.10074/) (2023)

## Abstract (arXiv)

Graph Convolutional Networks (GCNs) have been widely used due to their outstanding performance in processing graph-structured data. However, the undirected graphs limit their application scope. In this paper, we extend spectral-based graph convolution to directed graphs by using first- and second-order proximity, which can not only retain the connection properties of the directed graph, but also expand the receptive field of the convolution operation. A new GCN model, called DGCN, is then designed to learn representations on the directed graph, leveraging both the first- and second-order proximity information. We empirically show the fact that GCNs working only with DGCNs can encode more useful information from graph and help achieve better performance when generalized to other models. Moreover, extensive experiments on citation networks and co-purchase datasets demonstrate the superiority of our model against the state-of-the-art methods.