A Graph Convolution for Signed Directed Graphs
This work addresses the understudied challenge of signed directed graph analysis for researchers in graph learning, though it is incremental as it builds on existing spectral methods.
The paper tackles the problem of analyzing signed directed graphs by proposing a spectral graph convolution model that uses a novel complex Hermitian adjacency matrix to encode edge direction, sign, and connectivity, and it outperforms state-of-the-art techniques on four real-world datasets.
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.