  Edge perturbation is a basic method to modify graph structures. It can be
categorized into two veins based on their effects on the performance of graph
neural networks (GNNs), i.e., graph data augmentation and attack. Surprisingly,
both veins of edge perturbation methods employ the same operations, yet yield
opposite effects on GNNs' accuracy. A distinct boundary between these methods
in using edge perturbation has never been clearly defined. Consequently,
inappropriate perturbations may lead to undesirable outcomes, necessitating
precise adjustments to achieve desired effects. Therefore, questions of ``why
edge perturbation has a two-faced effect?'' and ``what makes edge perturbation
flexible and effective?'' still remain unanswered.
  In this paper, we will answer these questions by proposing a unified
formulation and establishing a clear boundary between two categories of edge
perturbation methods. Specifically, we conduct experiments to elucidate the
differences and similarities between these methods and theoretically unify the
workflow of these methods by casting it to one optimization problem. Then, we
devise Edge Priority Detector (EPD) to generate a novel priority metric,
bridging these methods up in the workflow. Experiments show that EPD can make
augmentation or attack flexibly and achieve comparable or superior performance
to other counterparts with less time overhead.
