# SDGNN: Learning Node Representation for Signed Directed Networks

arXiv: https://arxiv.org/abs/2101.02390 · HTML: https://mlsanity.com/paper/2101.02390/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 7 Jan 2021.

## Builds on (most cited first, 19 of 19)

- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [Community Interaction and Conflict on the Web](https://mlsanity.com/paper/1803.03697/) (2018)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [Learning Graph Representations with Embedding Propagation](https://mlsanity.com/paper/1710.03059/) (2017)
- [SNE: Signed Network Embedding](https://mlsanity.com/paper/1703.04837/) (2017)
- [Distributed Representations of Signed Networks](https://mlsanity.com/paper/1702.06819/) (2017)
- [Label-Consistency based Graph Neural Networks for Semi-supervised Node Classification](https://mlsanity.com/paper/2007.13435/) (2020)
- [On Spectral Analysis of Directed Signed Graphs](https://mlsanity.com/paper/1612.08102/) (2016)
- [Computing Lens for Exploring the Historical People's Social Network](https://mlsanity.com/paper/1907.09745/) (2019)

## Built on by (most cited first, 30 of 44)

- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [SigMaNet: One Laplacian to Rule Them All](https://mlsanity.com/paper/2205.13459/) (2022)
- [SSSNET: Semi-Supervised Signed Network Clustering](https://mlsanity.com/paper/2110.06623/) (2021)
- [Signed Bipartite Graph Neural Networks](https://mlsanity.com/paper/2108.09638/) (2021)
- [PyTorch Geometric Signed Directed: A Software Package on Graph Neural Networks for Signed and Directed Graphs](https://mlsanity.com/paper/2202.10793/) (2022)
- [Signed Graph Neural Networks: A Frequency Perspective](https://mlsanity.com/paper/2208.07323/) (2022)
- [Characterizing Polarization in Social Networks using the Signed Relational Latent Distance Model](https://mlsanity.com/paper/2301.09507/) (2023)
- [Self-Explainable Graph Transformer for Link Sign Prediction](https://mlsanity.com/paper/2408.08754/) (2024)
- [Representation Learning in Continuous-Time Dynamic Signed Networks](https://mlsanity.com/paper/2207.03408/) (2022)
- [SGPT: Few-Shot Prompt Tuning for Signed Graphs](https://mlsanity.com/paper/2412.12155/) (2024)
- [Large Language Models can Achieve Social Balance](https://mlsanity.com/paper/2410.04054/) (2024)
- [Signed Directed Graph Contrastive Learning with Laplacian Augmentation](https://mlsanity.com/paper/2301.05163/) (2023)
- [Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs](https://mlsanity.com/paper/2312.17361/) (2023)
- [Edge Classification on Graphs: New Directions in Topological Imbalance](https://mlsanity.com/paper/2406.11685/) (2024)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [MUSE: Multi-faceted Attention for Signed Network Embedding](https://mlsanity.com/paper/2104.14449/) (2021)
- [DropEdge not Foolproof: Effective Augmentation Method for Signed Graph Neural Networks](https://mlsanity.com/paper/2409.19620/) (2024)
- [GegenNet: Spectral Convolutional Neural Networks for Link Sign Prediction in Signed Bipartite Graphs](https://mlsanity.com/paper/2508.19907/) (2025)
- [A Graph Convolution for Signed Directed Graphs](https://mlsanity.com/paper/2208.11511/) (2022)
- [A Signed Subgraph Encoding Approach via Linear Optimization for Link Sign Prediction](https://mlsanity.com/paper/2305.09869/) (2023)
- [Learning Disentangled Representations in Signed Directed Graphs without Social Assumptions](https://mlsanity.com/paper/2307.03077/) (2023)
- [Mitigating Degree Bias in Signed Graph Neural Networks](https://mlsanity.com/paper/2408.08508/) (2024)
- [CSGDN: Contrastive Signed Graph Diffusion Network for Predicting Crop Gene-phenotype Associations](https://mlsanity.com/paper/2410.07511/) (2024)
- [The Signed Two-Space Proximity Model for Learning Representations in Protein-Protein Interaction Networks](https://mlsanity.com/paper/2503.03904/) (2025)
- [SigGAN : Adversarial Model for Learning Signed Relationships in Networks](https://mlsanity.com/paper/2201.06437/) (2022)
- [Trustworthiness-Driven Graph Convolutional Networks for Signed Network Embedding](https://mlsanity.com/paper/2309.00816/) (2023)
- [Towards Unified Modeling for Positive and Negative Preferences in Sign-Aware Recommendation](https://mlsanity.com/paper/2403.08246/) (2024)
- [Link Polarity Prediction from Sparse and Noisy Labels via Multiscale Social Balance](https://mlsanity.com/paper/2407.15643/) (2024)
- [A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction](https://mlsanity.com/paper/2601.19175/) (2026)
- [Nonlinear Laplacians Improve Signed-Directed Graph Learning](https://mlsanity.com/paper/2608.00836/) (2026)

## Abstract (arXiv)

Network embedding is aimed at mapping nodes in a network into low-dimensional vector representations. Graph Neural Networks (GNNs) have received widespread attention and lead to state-of-the-art performance in learning node representations. However, most GNNs only work in unsigned networks, where only positive links exist. It is not trivial to transfer these models to signed directed networks, which are widely observed in the real world yet less studied. In this paper, we first review two fundamental sociological theories (i.e., status theory and balance theory) and conduct empirical studies on real-world datasets to analyze the social mechanism in signed directed networks. Guided by related sociological theories, we propose a novel Signed Directed Graph Neural Networks model named SDGNN to learn node embeddings for signed directed networks. The proposed model simultaneously reconstructs link signs, link directions, and signed directed triangles. We validate our model's effectiveness on five real-world datasets, which are commonly used as the benchmark for signed network embedding. Experiments demonstrate the proposed model outperforms existing models, including feature-based methods, network embedding methods, and several GNN methods.