GRALE is a novel graph autoencoder proposed to address the challenges of graph-based learning. It encodes and decodes graphs of various sizes into a shared embedding space, utilizing a loss function inspired by Optimal Transport and a discriminative node matching module. It supports graph encoding and decoding using an attention-based architecture based on Evoformer, a core component of AlphaFold. GRALE enables highly general pretraining applicable to a wide range of downstream tasks, such as classification, regression, graph interpolation, editing, matching, and prediction, as demonstrated in experiments on simulated and molecular data.