# Directed Graph Auto-Encoders

arXiv: https://arxiv.org/abs/2202.12449 · HTML: https://mlsanity.com/paper/2202.12449/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 37 references that are in the map.
- First posted on arXiv 25 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Rethinking Knowledge Graph Propagation for Zero-Shot Learning](https://mlsanity.com/paper/1805.11724/) (2018)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [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)
- [Gravity-Inspired Graph Autoencoders for Directed Link Prediction](https://mlsanity.com/paper/1905.09570/) (2019)
- [edGNN: a Simple and Powerful GNN for Directed Labeled Graphs](https://mlsanity.com/paper/1904.08745/) (2019)

## Built on by (most cited first, 22 of 22)

- [Edge Directionality Improves Learning on Heterophilic Graphs](https://mlsanity.com/paper/2305.10498/) (2023)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Rethinking Reconstruction-based Graph-Level Anomaly Detection: Limitations and a Simple Remedy](https://mlsanity.com/paper/2410.20366/) (2024)
- [Conformal Load Prediction with Transductive Graph Autoencoders](https://mlsanity.com/paper/2406.08281/) (2024)
- [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)
- [DUPLEX: Dual GAT for Complex Embedding of Directed Graphs](https://mlsanity.com/paper/2406.05391/) (2024)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [Learning in Feature Spaces via Coupled Covariances: Asymmetric Kernel SVD and Nystr"om method](https://mlsanity.com/paper/2406.08748/) (2024)
- [DiRW: Path-Aware Digraph Learning for Heterophily](https://mlsanity.com/paper/2410.10320/) (2024)
- [Towards Data-centric Machine Learning on Directed Graphs: a Survey](https://mlsanity.com/paper/2412.01849/) (2024)
- [Residual Reweighted Conformal Prediction for Graph Neural Networks](https://mlsanity.com/paper/2506.07854/) (2025)
- [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)
- [Rethinking the positive role of cluster structure in complex networks for link prediction tasks](https://mlsanity.com/paper/2211.02396/) (2022)
- [GraphCroc: Cross-Correlation Autoencoder for Graph Structural Reconstruction](https://mlsanity.com/paper/2410.03396/) (2024)
- [Multi-Class and Multi-Task Strategies for Neural Directed Link Prediction](https://mlsanity.com/paper/2412.10895/) (2024)
- [Rethinking Link Prediction for Directed Graphs](https://mlsanity.com/paper/2502.05724/) (2025)
- [Toward Data-centric Directed Graph Learning: An Entropy-driven Approach](https://mlsanity.com/paper/2505.00983/) (2025)
- [Directed Link Prediction using GNN with Local and Global Feature Fusion](https://mlsanity.com/paper/2506.20235/) (2025)
- [MGKAN: Predicting Asymmetric Drug-Drug Interactions via a Multimodal Graph Kolmogorov-Arnold Network](https://mlsanity.com/paper/2602.01751/) (2026)
- [Subspace Projection Methods for Fast Spectral Embeddings of Evolving Graphs](https://mlsanity.com/paper/2603.19439/) (2026)

## Abstract (arXiv)

We introduce a new class of auto-encoders for directed graphs, motivated by a direct extension of the Weisfeiler-Leman algorithm to pairs of node labels. The proposed model learns pairs of interpretable latent representations for the nodes of directed graphs, and uses parameterized graph convolutional network (GCN) layers for its encoder and an asymmetric inner product decoder. Parameters in the encoder control the weighting of representations exchanged between neighboring nodes. We demonstrate the ability of the proposed model to learn meaningful latent embeddings and achieve superior performance on the directed link prediction task on several popular network datasets.