sMGC: A Complex-Valued Graph Convolutional Network via Magnetic Laplacian for Directed Graphs

Recent advancements in Graph Neural Networks have led to state-of-the-art performance on representation learning of graphs for node classification. However, the majority of existing works process directed graphs by symmetrization, which may cause loss of directional information. In this paper, we propose the magnetic Laplacian that preserves edge directionality by encoding it into complex phase as a deformation of the combinatorial Laplacian. In addition, we design an Auto-Regressive Moving-Average (ARMA) filter that is capable of learning global features from graphs. To reduce time complexity, Taylor expansion is applied to approximate the filter. We derive complex-valued operations in graph neural network and devise a simplified Magnetic Graph Convolution network, namely sMGC. Our experiment results demonstrate that sMGC is a fast, powerful, and widely applicable GNN.