GSN: A Universal Graph Neural Network Inspired by Spring Network

The design of universal Graph Neural Networks (GNNs) that operate on both homophilous and heterophilous graphs has received increased research attention in recent years. Existing heterophilous GNNs, particularly those designed in the spatial domain, lack a convincing theoretical or physical motivation. In this paper, we propose the Graph Spring Network (GSN), a universal GNN model that works for both homophilous and heterophilous graphs, inspired by spring networks and metric learning. We show that the GSN framework interprets many existing GNN models from the perspective of spring potential energy minimization with various metrics, which gives these models strong physical motivations. We also conduct extensive experiments to demonstrate our GSN framework's superior performance on real-world homophilous and heterophilous data sets.