MSGCN: Multiplex Spatial Graph Convolution Network for Interlayer Link Weight Prediction

Graph Neural Networks (GNNs) have been widely used for various learning tasks, ranging from node classification to link prediction. They have demonstrated excellent performance in multiple domains involving graph-structured data. However, an important but less explored learning task is link weight prediction which is more complex than binary link classification. Link weight prediction becomes even more challenging when considering multilayer networks, where nodes can be connected across multiple layers. To address these challenges, we propose a new method called Multiplex Spatial Graph Convolution Network (MSGCN), which spatially embeds information across multiple layers to predict interlayer link weights. The MSGCN method generalizes spatial graph convolution to multiplex networks and captures the geometric structure of nodes across multiple layers. Extensive experiments using data with known interlayer link information show that the MSGCN model has robust, accurate, and generalizable link weight prediction performance across a wide variety of network structures. We also demonstrate a real-world application of the proposed method using the London transportation network. In this setting, MSGCN accurately predicts passenger loads in the multiplex network, where the interlayer link weights represent the number of passengers traveling between stations that are not directly connected.