  Self-supervised learning of graph neural networks (GNNs) aims to learn an
accurate representation of the graphs in an unsupervised manner, to obtain
transferable representations of them for diverse downstream tasks. Predictive
learning and contrastive learning are the two most prevalent approaches for
graph self-supervised learning. However, they have their own drawbacks. While
the predictive learning methods can learn the contextual relationships between
neighboring nodes and edges, they cannot learn global graph-level similarities.
Contrastive learning, while it can learn global graph-level similarities, its
objective to maximize the similarity between two differently perturbed graphs
may result in representations that cannot discriminate two similar graphs with
different properties. To tackle such limitations, we propose a framework that
aims to learn the exact discrepancy between the original and the perturbed
graphs, coined as Discrepancy-based Self-supervised LeArning (D-SLA).
Specifically, we create multiple perturbations of the given graph with varying
degrees of similarity, and train the model to predict whether each graph is the
original graph or the perturbed one. Moreover, we further aim to accurately
capture the amount of discrepancy for each perturbed graph using the graph edit
distance. We validate our D-SLA on various graph-related downstream tasks,
including molecular property prediction, protein function prediction, and link
prediction tasks, on which ours largely outperforms relevant baselines.
