# LightDiC: A Simple yet Effective Approach for Large-scale Digraph Representation Learning

arXiv: https://arxiv.org/abs/2401.11772 · HTML: https://mlsanity.com/paper/2401.11772/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 22 Jan 2024.

## Builds on (most cited first, 30 of 33)

- [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)
- [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)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification](https://mlsanity.com/paper/2009.03509/) (2020)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Rumor Detection on Social Media with Bi-Directional Graph Convolutional Networks](https://mlsanity.com/paper/2001.06362/) (2020)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Specformer: Spectral Graph Neural Networks Meet Transformers](https://mlsanity.com/paper/2303.01028/) (2023)
- [Graph Convolutional Networks with EigenPooling](https://mlsanity.com/paper/1904.13107/) (2019)
- [Scalable Graph Neural Networks via Bidirectional Propagation](https://mlsanity.com/paper/2010.15421/) (2020)
- [Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisited](https://mlsanity.com/paper/2202.03580/) (2022)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [Hierarchical Graph Pooling with Structure Learning](https://mlsanity.com/paper/1911.05954/) (2019)
- [PaSca: a Graph Neural Architecture Search System under the Scalable Paradigm](https://mlsanity.com/paper/2203.00638/) (2022)
- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [Magnetic Eigenmaps for the Visualization of Directed Networks](https://mlsanity.com/paper/1606.08266/) (2016)
- [Magnetic eigenmaps for community detection in directed networks](https://mlsanity.com/paper/1606.07359/) (2016)
- [DIGRAC: Digraph Clustering Based on Flow Imbalance](https://mlsanity.com/paper/2106.05194/) (2021)
- [Finding large balanced subgraphs in signed networks](https://mlsanity.com/paper/2002.00775/) (2020)
- [Generating Simple Directed Social Network Graphs for Information Spreading](https://mlsanity.com/paper/2205.02485/) (2022)

## Built on by (most cited first, 11 of 11)

- [OpenFGL: A Comprehensive Benchmark for Federated Graph Learning](https://mlsanity.com/paper/2408.16288/) (2024)
- [Toward General and Robust LLM-enhanced Text-attributed Graph Learning](https://mlsanity.com/paper/2504.02343/) (2025)
- [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)
- [Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach](https://mlsanity.com/paper/2501.11817/) (2025)
- [Toward Scalable Graph Unlearning: A Node Influence Maximization based Approach](https://mlsanity.com/paper/2501.11823/) (2025)
- [ScaDyG:A New Paradigm for Large-scale Dynamic Graph Learning](https://mlsanity.com/paper/2501.16002/) (2025)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [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)
- [GravityGraphSAGE: Link Prediction in Directed Attributed Graphs](https://mlsanity.com/paper/2605.09408/) (2026)

## Abstract (arXiv)

Most existing graph neural networks (GNNs) are limited to undirected graphs, whose restricted scope of the captured relational information hinders their expressive capabilities and deployments in real-world scenarios. Compared with undirected graphs, directed graphs (digraphs) fit the demand for modeling more complex topological systems by capturing more intricate relationships between nodes, such as formulating transportation and financial networks. While some directed GNNs have been introduced, their inspiration mainly comes from deep learning architectures, which lead to redundant complexity and computation, making them inapplicable to large-scale databases. To address these issues, we propose LightDiC, a scalable variant of the digraph convolution based on the magnetic Laplacian. Since topology-related computations are conducted solely during offline pre-processing, LightDiC achieves exceptional scalability, enabling downstream predictions to be trained separately without incurring recursive computational costs. Theoretical analysis shows that LightDiC utilizes directed information to achieve message passing based on the complex field, which corresponds to the proximal gradient descent process of the Dirichlet energy optimization function from the perspective of digraph signal denoising, ensuring its expressiveness. Experimental results demonstrate that LightDiC performs comparably well or even outperforms other SOTA methods in various downstream tasks, with fewer learnable parameters and higher training efficiency. Notably, LightDiC is the first DiGNN to provide satisfactory results in the most representative large-scale database (ogbn-papers100M).