# Signed Directed Graph Contrastive Learning with Laplacian Augmentation

arXiv: https://arxiv.org/abs/2301.05163 · HTML: https://mlsanity.com/paper/2301.05163/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 12 Jan 2023.

## Builds on (most cited first, 30 of 34)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [LightGCN: Simplifying and Powering Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2002.02126/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Graph Neural Networks for Social Recommendation](https://mlsanity.com/paper/1902.07243/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [SimGRACE: A Simple Framework for Graph Contrastive Learning without Data Augmentation](https://mlsanity.com/paper/2202.03104/) (2022)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning](https://mlsanity.com/paper/2202.06200/) (2022)
- [Multi-view Contrastive Graph Clustering](https://mlsanity.com/paper/2110.11842/) (2021)
- [Contrastive Explanations for Model Interpretability](https://mlsanity.com/paper/2103.01378/) (2021)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [Contrastive Self-supervised Learning for Graph Classification](https://mlsanity.com/paper/2009.05923/) (2020)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [Graph Contrastive Clustering](https://mlsanity.com/paper/2104.01429/) (2021)
- [GeomGCL: Geometric Graph Contrastive Learning for Molecular Property Prediction](https://mlsanity.com/paper/2109.11730/) (2021)
- [SDGNN: Learning Node Representation for Signed Directed Networks](https://mlsanity.com/paper/2101.02390/) (2021)
- [Multi-view Graph Contrastive Representation Learning for Drug-Drug Interaction Prediction](https://mlsanity.com/paper/2010.11711/) (2020)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [SigMaNet: One Laplacian to Rule Them All](https://mlsanity.com/paper/2205.13459/) (2022)
- [The Slashdot Zoo: Mining a Social Network with Negative Edges](https://mlsanity.com/paper/1710.11395/) (2017)

## Built on by (most cited first, 4 of 4)

- [Shared Growth of Graph Neural Networks via Prompted Free-direction Knowledge Distillation](https://mlsanity.com/paper/2307.00534/) (2023)
- [Toward General Digraph Contrastive Learning: A Dual Spatial Perspective](https://mlsanity.com/paper/2510.16311/) (2025)
- [Adaptive Branch Specialization in Spectral-Spatial Graph Neural Networks for Certified Robustness](https://mlsanity.com/paper/2505.08320/) (2025)
- [ChemHyperMag: Physics-informed magnetic hypergraph learning improves molecular ADMET prediction](https://mlsanity.com/paper/2607.18332/) (2026)

## Abstract (arXiv)

Graph contrastive learning has become a powerful technique for several graph mining tasks. It learns discriminative representation from different perspectives of augmented graphs. Ubiquitous in our daily life, singed-directed graphs are the most complex and tricky to analyze among various graph types. That is why singed-directed graph contrastive learning has not been studied much yet, while there are many contrastive studies for unsigned and undirected. Thus, this paper proposes a novel signed-directed graph contrastive learning, SDGCL. It makes two different structurally perturbed graph views and gets node representations via magnetic Laplacian perturbation. We use a node-level contrastive loss to maximize the mutual information between the two graph views. The model is jointly learned with contrastive and supervised objectives. The graph encoder of SDGCL does not depend on social theories or predefined assumptions. Therefore it does not require finding triads or selecting neighbors to aggregate. It leverages only the edge signs and directions via magnetic Laplacian. To the best of our knowledge, it is the first to introduce magnetic Laplacian perturbation and signed spectral graph contrastive learning. The superiority of the proposed model is demonstrated through exhaustive experiments on four real-world datasets. SDGCL shows better performance than other state-of-the-art on four evaluation metrics.