# Node Representation Learning for Directed Graphs

arXiv: https://arxiv.org/abs/1810.09176 · HTML: https://mlsanity.com/paper/1810.09176/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2018.

## Built on by (most cited first, 16 of 16)

- [A Broader Picture of Random-walk Based Graph Embedding](https://mlsanity.com/paper/2110.12344/) (2021)
- [WGCN: Graph Convolutional Networks with Weighted Structural Features](https://mlsanity.com/paper/2104.14060/) (2021)
- [Learning with Asymmetric Kernels: Least Squares and Feature Interpretation](https://mlsanity.com/paper/2202.01397/) (2022)
- [Multi-label Node Classification On Graph-Structured Data](https://mlsanity.com/paper/2304.10398/) (2023)
- [A Robust and Generalized Framework for Adversarial Graph Embedding](https://mlsanity.com/paper/2105.10651/) (2021)
- [D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning](https://mlsanity.com/paper/2112.11734/) (2021)
- [Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding](https://mlsanity.com/paper/2503.18010/) (2025)
- [Random Fourier Features for Asymmetric Kernels](https://mlsanity.com/paper/2209.08461/) (2022)
- [DUPLEX: Dual GAT for Complex Embedding of Directed Graphs](https://mlsanity.com/paper/2406.05391/) (2024)
- [A Multi-purposed Unsupervised Framework for Comparing Embeddings of Undirected and Directed Graphs](https://mlsanity.com/paper/2112.00075/) (2021)
- [Recommending Related Products Using Graph Neural Networks in Directed Graphs](https://mlsanity.com/paper/2211.11583/) (2022)
- [Privacy and Transparency in Graph Machine Learning: A Unified Perspective](https://mlsanity.com/paper/2207.10896/) (2022)
- [Nonlinear SVD with Asymmetric Kernels: feature learning and asymmetric Nystr"om method](https://mlsanity.com/paper/2306.07040/) (2023)
- [BHGNN-RT: Network embedding for directed heterogeneous graphs](https://mlsanity.com/paper/2311.14404/) (2023)
- [Rethinking the positive role of cluster structure in complex networks for link prediction tasks](https://mlsanity.com/paper/2211.02396/) (2022)
- [Rethinking Link Prediction for Directed Graphs](https://mlsanity.com/paper/2502.05724/) (2025)

## Abstract (arXiv)

We propose a novel approach for learning node representations in directed graphs, which maintains separate views or embedding spaces for the two distinct node roles induced by the directionality of the edges. We argue that the previous approaches either fail to encode the edge directionality or their encodings cannot be generalized across tasks. With our simple alternating random walk strategy, we generate role specific vertex neighborhoods and train node embeddings in their corresponding source/target roles while fully exploiting the semantics of directed graphs. We also unearth the limitations of evaluations on directed graphs in previous works and propose a clear strategy for evaluating link prediction and graph reconstruction in directed graphs. We conduct extensive experiments to showcase our effectiveness on several real-world datasets on link prediction, node classification and graph reconstruction tasks. We show that the embeddings from our approach are indeed robust, generalizable and well performing across multiple kinds of tasks and graphs. We show that we consistently outperform all baselines for node classification task. In addition to providing a theoretical interpretation of our method we also show that we are considerably more robust than the other directed graph approaches.