# Signed Graph Neural Networks: A Frequency Perspective

arXiv: https://arxiv.org/abs/2208.07323 · HTML: https://mlsanity.com/paper/2208.07323/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 48 references that are in the map.
- First posted on arXiv 15 Aug 2022.

## Builds on (most cited first, 24 of 24)

- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Signed Graph Attention Networks](https://mlsanity.com/paper/1906.10958/) (2019)
- [SDGNN: Learning Node Representation for Signed Directed Networks](https://mlsanity.com/paper/2101.02390/) (2021)
- [Exploiting Social Network Structure for Person-to-Person Sentiment Analysis](https://mlsanity.com/paper/1409.2450/) (2014)
- [Magnetic Eigenmaps for the Visualization of Directed Networks](https://mlsanity.com/paper/1606.08266/) (2016)
- [SPONGE: A generalized eigenproblem for clustering signed networks](https://mlsanity.com/paper/1904.08575/) (2019)
- [Magnetic eigenmaps for community detection in directed networks](https://mlsanity.com/paper/1606.07359/) (2016)
- [SSSNET: Semi-Supervised Signed Network Clustering](https://mlsanity.com/paper/2110.06623/) (2021)
- [Distributed Representations of Signed Networks](https://mlsanity.com/paper/1702.06819/) (2017)
- [VEWS: A Wikipedia Vandal Early Warning System](https://mlsanity.com/paper/1507.01272/) (2015)
- [The Slashdot Zoo: Mining a Social Network with Negative Edges](https://mlsanity.com/paper/1710.11395/) (2017)
- [Graph Signal Processing and Deep Learning: Convolution, Pooling, and Topology](https://mlsanity.com/paper/2008.01247/) (2020)
- [On spectral partitioning of signed graphs](https://mlsanity.com/paper/1701.01394/) (2017)

## Built on by (most cited first, 10 of 10)

- [MSGNN: A Spectral Graph Neural Network Based on a Novel Magnetic Signed Laplacian](https://mlsanity.com/paper/2209.00546/) (2022)
- [Signed Directed Graph Contrastive Learning with Laplacian Augmentation](https://mlsanity.com/paper/2301.05163/) (2023)
- [Signed Graph Autoencoder for Explainable and Polarization-Aware Network Embeddings](https://mlsanity.com/paper/2409.10452/) (2024)
- [Link Polarity Prediction from Sparse and Noisy Labels via Multiscale Social Balance](https://mlsanity.com/paper/2407.15643/) (2024)
- [DLGNet: Hyperedge Classification through Directed Line Graphs for Chemical Reactions](https://mlsanity.com/paper/2410.06969/) (2024)
- [Haar-Laplacian for directed graphs](https://mlsanity.com/paper/2411.15527/) (2024)
- [Nonlinear Laplacians Improve Signed-Directed Graph Learning](https://mlsanity.com/paper/2608.00836/) (2026)
- [Federated Spectral Graph Transformers Meet Neural Ordinary Differential Equations for Non-IID Graphs](https://mlsanity.com/paper/2504.11808/) (2025)
- [Learning from Heterophilic Graphs: A Spectral Theory Perspective on the Impact of Self-Loops and Parallel Edges](https://mlsanity.com/paper/2509.13139/) (2025)
- [DualSpectralCF: Training-Free Sign-Aware Spectral Collaborative Filtering](https://mlsanity.com/paper/2608.10247/) (2026)

## Abstract (arXiv)

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains high-frequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.