# Asymmetric Graph Representation Learning

arXiv: https://arxiv.org/abs/2110.07436 · HTML: https://mlsanity.com/paper/2110.07436/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 41 references that are in the map.
- First posted on arXiv 14 Oct 2021.

## Builds on (most cited first, 30 of 30)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [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)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Graph Convolutional Networks for Text Classification](https://mlsanity.com/paper/1809.05679/) (2018)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Directional Graph Networks](https://mlsanity.com/paper/2010.02863/) (2020)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [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)
- [Multi-hop Attention Graph Neural Network](https://mlsanity.com/paper/2009.14332/) (2020)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Column Networks for Collective Classification](https://mlsanity.com/paper/1609.04508/) (2016)

## Built on by (most cited first, 1 of 1)

- [A Network Science perspective of Graph Convolutional Networks: A survey](https://mlsanity.com/paper/2301.04824/) (2023)

## Abstract (arXiv)

Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth). However, there is a vast amount of applications where the information flow is asymmetric, leading to directed graphs where information can only be passed in one direction. For example, a directed edge indicates that the information can only be conveyed forwardly from the start node to the end node, but not backwardly. To accommodate such an asymmetric structure of directed graphs within the framework of GNNs, we propose a simple yet remarkably effective framework for directed graph analysis to incorporate such one-way information passing. We define an incoming embedding and an outgoing embedding for each node to model its sending and receiving features respectively. We further develop two steps in our directed GNN model with the first one to aggregate/update the incoming features of nodes and the second one to aggregate/update the outgoing features. By imposing the two roles for each node, the likelihood of a directed edge can be calculated based on the outgoing embedding of the start node and the incoming embedding of the end node. The log-likelihood of all edges plays a natural role of regularization for the proposed model, which can alleviate the over-smoothing problem of the deep GNNs. Extensive experiments on multiple real-world directed graphs demonstrate outstanding performances of the proposed model in both node-level and graph-level tasks.