  We introduce a randomized topological augmentor based on Schur complements
for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the
technique generates unbiased approximations of its Schur complements and treats
the corresponding graphs as augmented views. We discuss the benefits of our
approach, provide theoretical justifications and present connections with graph
diffusion. Unlike previous efforts, we study the empirical effectiveness of the
augmentor in a controlled fashion by varying the design choices for subsequent
GCL phases, such as encoding and contrasting. Extensive experiments on node and
graph classification benchmarks demonstrate that our technique consistently
outperforms pre-defined and adaptive augmentation approaches to achieve
state-of-the-art results.
