  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.
