# A Graph Convolution for Signed Directed Graphs

arXiv: https://arxiv.org/abs/2208.11511 · HTML: https://mlsanity.com/paper/2208.11511/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 49 references that are in the map.
- First posted on arXiv 23 Aug 2022.

## Builds on (most cited first, 22 of 22)

- [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)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [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)
- [Spectral-based Graph Convolutional Network for Directed Graphs](https://mlsanity.com/paper/1907.08990/) (2019)
- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [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)
- [Signed Graph Diffusion Network](https://mlsanity.com/paper/2012.14191/) (2020)
- [The Slashdot Zoo: Mining a Social Network with Negative Edges](https://mlsanity.com/paper/1710.11395/) (2017)
- [Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian](https://mlsanity.com/paper/2007.03466/) (2020)
- [A Note on Markov Normalized Magnetic Eigenmaps](https://mlsanity.com/paper/1608.04418/) (2016)

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

- [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)

## Abstract (arXiv)

A signed directed graph is a graph with sign and direction information on the edges. Even though signed directed graphs are more informative than unsigned or undirected graphs, they are more complicated to analyze and have received less research attention. This paper investigates a spectral graph convolution model to fully utilize the information embedded in signed directed edges. We propose a novel complex Hermitian adjacency matrix that encodes graph information via complex numbers. Compared to a simple connection-based adjacency matrix, the complex Hermitian can represent edge direction, sign, and connectivity via its phases and magnitudes. Then, we define a magnetic Laplacian of the proposed adjacency matrix and prove that it is positive semi-definite (PSD) for the analyses using spectral graph convolution. We perform extensive experiments on four real-world datasets. Our experiments show that the proposed scheme outperforms several state-of-the-art techniques.