Renormalized Graph Representations for Node Classification

Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using various coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node classification tasks. At the core of the theory is the grouping of nodes connected by significant information flow at a given time scale. Representations of the graph at different scales encode interaction information at different ranges. We specifically experiment using representations at the characteristic scale of the graph’s mesoscopic structures. We provide the models with the original graph and the graph represented at the characteristic resolution scale and compare them to models that can only access the original graph. Our results showed that models with access to both the original graph and the characteristic scale graph can achieve statistically significant improvements in test accuracy.