  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.
