# A Simple and Scalable Graph Neural Network for Large Directed Graphs

arXiv: https://arxiv.org/abs/2306.08274 · HTML: https://mlsanity.com/paper/2306.08274/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 30 of 31)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Adaptive Universal Generalized PageRank Graph Neural Network](https://mlsanity.com/paper/2006.07988/) (2020)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [A critical look at the evaluation of GNNs under heterophily: Are we really making progress?](https://mlsanity.com/paper/2302.11640/) (2023)
- [Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methods](https://mlsanity.com/paper/2110.14446/) (2021)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [Finding Global Homophily in Graph Neural Networks When Meeting Heterophily](https://mlsanity.com/paper/2205.07308/) (2022)
- [Revisiting Heterophily For Graph Neural Networks](https://mlsanity.com/paper/2210.07606/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [EEG-Based Emotion Recognition Using Regularized Graph Neural Networks](https://mlsanity.com/paper/1907.07835/) (2019)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [GraphWorld: Fake Graphs Bring Real Insights for GNNs](https://mlsanity.com/paper/2203.00112/) (2022)
- [A Comprehensive Study on Large-Scale Graph Training: Benchmarking and Rethinking](https://mlsanity.com/paper/2210.07494/) (2022)
- [Improving Graph Neural Networks with Simple Architecture Design](https://mlsanity.com/paper/2105.07634/) (2021)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Beyond Real-world Benchmark Datasets: An Empirical Study of Node Classification with GNNs](https://mlsanity.com/paper/2206.09144/) (2022)
- [Deep Graph Neural Networks with Shallow Subgraph Samplers](https://mlsanity.com/paper/2012.01380/) (2020)
- [GNNRank: Learning Global Rankings from Pairwise Comparisons via Directed Graph Neural Networks](https://mlsanity.com/paper/2202.00211/) (2022)

## Built on by (most cited first, 2 of 2)

- [Explainable Graph Neural Architecture Search via Monte-Carlo Tree Search (Full version)](https://mlsanity.com/paper/2308.15734/) (2023)
- [Graph Neural Network leveraging Higher-order Class Label Connectivity for Heterophilous Graphs](https://mlsanity.com/paper/2606.07475/) (2026)

## Abstract (arXiv)

Node classification is one of the hottest tasks in graph analysis. Though existing studies have explored various node representations in directed and undirected graphs, they have overlooked the distinctions of their capabilities to capture the information of graphs. To tackle the limitation, we investigate various combinations of node representations (aggregated features vs. adjacency lists) and edge direction awareness within an input graph (directed vs. undirected). We address the first empirical study to benchmark the performance of various GNNs that use either combination of node representations and edge direction awareness. Our experiments demonstrate that no single combination stably achieves state-of-the-art results across datasets, which indicates that we need to select appropriate combinations depending on the dataset characteristics. In response, we propose a simple yet holistic classification method A2DUG which leverages all combinations of node representations in directed and undirected graphs. We demonstrate that A2DUG stably performs well on various datasets and improves the accuracy up to 11.29 compared with the state-of-the-art methods. To spur the development of new methods, we publicly release our complete codebase under the MIT license.