# Toward Effective Digraph Representation Learning: A Magnetic Adaptive Propagation based Approach

arXiv: https://arxiv.org/abs/2501.11817 · HTML: https://mlsanity.com/paper/2501.11817/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 67 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Builds on (most cited first, 30 of 37)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [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)
- [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)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Datasets: A Community Library for Natural Language Processing](https://mlsanity.com/paper/2109.02846/) (2021)
- [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)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [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)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [Rumor Detection on Social Media with Bi-Directional Graph Convolutional Networks](https://mlsanity.com/paper/2001.06362/) (2020)
- [NAGphormer: A Tokenized Graph Transformer for Node Classification in Large Graphs](https://mlsanity.com/paper/2206.04910/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Directed Acyclic Graph Neural Networks](https://mlsanity.com/paper/2101.07965/) (2021)
- [Scalable and Adaptive Graph Neural Networks with Self-Label-Enhanced training](https://mlsanity.com/paper/2104.09376/) (2021)
- [Graph Neural Networks with Learnable and Optimal Polynomial Bases](https://mlsanity.com/paper/2302.12432/) (2023)
- [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)
- [HoloNets: Spectral Convolutions do extend to Directed Graphs](https://mlsanity.com/paper/2310.02232/) (2023)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [ROD: Reception-aware Online Distillation for Sparse Graphs](https://mlsanity.com/paper/2107.11789/) (2021)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [Rethinking Node-wise Propagation for Large-scale Graph Learning](https://mlsanity.com/paper/2402.06128/) (2024)

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

- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [AdvSynGNN: Structure-Adaptive Graph Neural Nets via Adversarial Synthesis and Self-Corrective Propagation](https://mlsanity.com/paper/2602.17071/) (2026)

## Abstract (arXiv)

The q-parameterized magnetic Laplacian serves as the foundation of directed graph (digraph) convolution, enabling this kind of digraph neural network (MagDG) to encode node features and structural insights by complex-domain message passing. As a generalization of undirected methods, MagDG shows superior capability in modeling intricate web-scale topology. Despite the great success achieved by existing MagDGs, limitations still exist: (1) Hand-crafted q: The performance of MagDGs depends on selecting an appropriate q-parameter to construct suitable graph propagation equations in the complex domain. This parameter tuning, driven by downstream tasks, limits model flexibility and significantly increases manual effort. (2) Coarse Message Passing: Most approaches treat all nodes with the same complex-domain propagation and aggregation rules, neglecting their unique digraph contexts. This oversight results in sub-optimal performance. To address the above issues, we propose two key techniques: (1) MAP is crafted to be a plug-and-play complex-domain propagation optimization strategy in the context of digraph learning, enabling seamless integration into any MagDG to improve predictions while enjoying high running efficiency. (2) MAP++ is a new digraph learning framework, further incorporating a learnable mechanism to achieve adaptively edge-wise propagation and node-wise aggregation in the complex domain for better performance. Extensive experiments on 12 datasets demonstrate that MAP enjoys flexibility for it can be incorporated with any MagDG, and scalability as it can deal with web-scale digraphs. MAP++ achieves SOTA predictive performance on 4 different downstream tasks.