GSN: A Graph Neural Network Inspired by Spring Network

The design of Graph Neural Networks (GNNs) that operate on both homophilous and heterophilous graphs has received research attention in recent years. Existing heterophilous GNNs, particularly those designed in the spatial domain, lack a convincing theoretical or physical motivation. Inspired by an old-fashioned spring network model, we propose the Graph Spring Network (GSN), a universal GNN model that works for homophilous and heterophilous graphs. We show that the GSN framework can interpret many GNN models from the perspective of potential energy minimization of a spring network with respect to various metrics, which entrusts strong physical motivations to these models. We also conduct experiments to demonstrate the performance of our GSN model on real-world datasets.