Recent studies have shown that Graph Convolutional Networks (GCNs) are
vulnerable to adversarial attacks on the graph structure. Although multiple
works have been proposed to improve their robustness against such structural
adversarial attacks, the reasons for the success of the attacks remain unclear.
In this work, we theoretically and empirically demonstrate that structural
adversarial examples can be attributed to the non-robust aggregation scheme
(i.e., the weighted mean) of GCNs. Specifically, our analysis takes advantage
of the breakdown point which can quantitatively measure the robustness of
aggregation schemes. The key insight is that weighted mean, as the basic design
of GCNs, has a low breakdown point and its output can be dramatically changed
by injecting a single edge. We show that adopting the aggregation scheme with a
high breakdown point (e.g., median or trimmed mean) could significantly enhance
the robustness of GCNs against structural attacks. Extensive experiments on
four real-world datasets demonstrate that such a simple but effective method
achieves the best robustness performance compared to state-of-the-art models.

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