MGC: A Complex-Valued Graph Convolutional Network for Directed Graphs
This addresses a specific bottleneck in graph representation learning for directed graphs, offering a novel method that is incremental but improves upon existing approaches.
The paper tackled the problem of processing directed graphs in Graph Neural Networks, which often lose directional information through symmetrization, by proposing a complex-valued graph convolutional network (MGC) that uses a magnetic Laplacian to preserve edge directionality, achieving fast and powerful performance on directed homogeneous and heterogeneous graph datasets.
Recent advancements in Graph Neural Networks have led to state-of-the-art performance on graph representation learning. However, the majority of existing works process directed graphs by symmetrization, which causes loss of directional information. To address this issue, we introduce the magnetic Laplacian, a discrete Schrödinger operator with magnetic field, which preserves edge directionality by encoding it into a complex phase with an electric charge parameter. By adopting a truncated variant of PageRank named Linear- Rank, we design and build a low-pass filter for homogeneous graphs and a high-pass filter for heterogeneous graphs. In this work, we propose a complex-valued graph convolutional network named Magnetic Graph Convolutional network (MGC). With the corresponding complex-valued techniques, we ensure our model will be degenerated into real-valued when the charge parameter is in specific values. We test our model on several graph datasets including directed homogeneous and heterogeneous graphs. The experimental results demonstrate that MGC is fast, powerful, and widely applicable.