  In recent years, Graph Contrastive Learning (GCL) has shown remarkable
effectiveness in learning representations on graphs. As a component of GCL,
good augmentation views are supposed to be invariant to the important
information while discarding the unimportant part. Existing augmentation views
with perturbed graph structures are usually based on random topology corruption
in the spatial domain; however, from perspectives of the spectral domain, this
approach may be ineffective as it fails to pose tailored impacts on the
information of different frequencies, thus weakening the agreement between the
augmentation views. By a preliminary experiment, we show that the impacts
caused by spatial random perturbation are approximately evenly distributed
among frequency bands, which may harm the invariance of augmentations required
by contrastive learning frameworks. To address this issue, we argue that the
perturbation should be selectively posed on the information concerning
different frequencies. In this paper, we propose GASSER which poses tailored
perturbation on the specific frequencies of graph structures in spectral
domain, and the edge perturbation is selectively guided by the spectral hints.
As shown by extensive experiments and theoretical analysis, the augmentation
views are adaptive and controllable, as well as heuristically fitting the
homophily ratios and spectrum of graph structures.
