Analyzing the vulnerability of power systems in cascading failures is generally regarded as a challenging problem. Although existing studies can extract some critical rules, they fail to capture the complex subtleties under different operational conditions. In recent years, several deep learning methods have been applied to address this issue. However, most of the existing deep learning methods consider only the grid topology of a power system in terms of topological connections, but do not encompass a power system’s spatial information such as the electrical distance to increase the accuracy in the process of graph convolution. In this paper, we construct a novel power-weighted line graph that uses power system topology and spatial information to optimize the edge weight assignment of the line graph. Then we propose a multi-graph convolutional network (MGCN) based on a graph classification task, which preserves a power system’s spatial correlations and captures the relationships among physical components. Our model can better handle the problem with power systems that have parallel lines, where our method can maintain desirable accuracy in modeling systems with these extra topology features. To increase the interpretability of the model, we present the MGCN using layer-wise relevance propagation and quantify the contributing factors of model classification.