  Recent studies show that Graph Neural Networks (GNNs) are vulnerable to
adversarial attack, i.e., an imperceptible structure perturbation can fool GNNs
to make wrong predictions. Some researches explore specific properties of clean
graphs such as the feature smoothness to defense the attack, but the analysis
of it has not been well-studied. In this paper, we analyze the adversarial
attack on graphs from the perspective of feature smoothness which further
contributes to an efficient new adversarial defensive algorithm for GNNs. We
discover that the effect of the high-order graph structure is a smoother filter
for processing graph structures. Intuitively, the high-order graph structure
denotes the path number between nodes, where larger number indicates closer
connection, so it naturally contributes to defense the adversarial
perturbation. Further, we propose a novel algorithm that incorporates the
high-order structural information into the graph structure learning. We perform
experiments on three popular benchmark datasets, Cora, Citeseer and Polblogs.
Extensive experiments demonstrate the effectiveness of our method for defending
against graph adversarial attacks.
