Empowering Simple Graph Convolutional Networks

Many neural networks for graphs are based on the graph convolution (GC) operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, which tend to add complexity (and nonlinearity) to the model. Recently, however, a simplified GC operator, dubbed simple graph convolution (SGC), which aims to remove nonlinearities was proposed. Motivated by the good results reached by this simpler model, in this article we propose, analyze, and compare simple graph convolution operators of increasing complexity that rely on linear transformations or controlled nonlinearities, and that can be implemented in single-layer graph convolutional networks (GCNs). Their computational expressiveness is characterized as well. We show that the predictive performance of the proposed GC operators is competitive with the ones of other widely adopted models on the considered node classification benchmark datasets.