  Recent studies have shown that attackers can catastrophically reduce the
performance of GNNs by maliciously modifying the graph structure or node
features on the graph. Adversarial training, which has been shown to be one of
the most effective defense mechanisms against adversarial attacks in computer
vision, holds great promise for enhancing the robustness of GNNs. There is
limited research on defending against attacks by performing adversarial
training on graphs, and it is crucial to delve deeper into this approach to
optimize its effectiveness. Therefore, based on robust adversarial training on
graphs, we propose a hierarchical constraint refinement framework (HC-Ref) that
enhances the anti-perturbation capabilities of GNNs and downstream classifiers
separately, ultimately leading to improved robustness. We propose corresponding
adversarial regularization terms that are conducive to adaptively narrowing the
domain gap between the normal part and the perturbation part according to the
characteristics of different layers, promoting the smoothness of the predicted
distribution of both parts. Moreover, existing research on graph robust
adversarial training primarily concentrates on training from the standpoint of
node feature perturbations and seldom takes into account alterations in the
graph structure. This limitation makes it challenging to prevent attacks based
on topological changes in the graph. This paper generates adversarial examples
by utilizing graph structure perturbations, offering an effective approach to
defend against attack methods that are based on topological changes. Extensive
experiments on two real-world graph benchmarks show that HC-Ref successfully
resists various attacks and has better node classification performance compared
to several baseline methods.
