  While deep neural networks have achieved great success in graph analysis,
recent work has shown that they are vulnerable to adversarial attacks. Compared
with adversarial attacks on image classification, performing adversarial
attacks on graphs is more challenging because of the discrete and
non-differential nature of the adjacent matrix for a graph. In this work, we
propose Cluster Attack -- a Graph Injection Attack (GIA) on node
classification, which injects fake nodes into the original graph to degenerate
the performance of graph neural networks (GNNs) on certain victim nodes while
affecting the other nodes as little as possible. We demonstrate that a GIA
problem can be equivalently formulated as a graph clustering problem; thus, the
discrete optimization problem of the adjacency matrix can be solved in the
context of graph clustering. In particular, we propose to measure the
similarity between victim nodes by a metric of Adversarial Vulnerability, which
is related to how the victim nodes will be affected by the injected fake node,
and to cluster the victim nodes accordingly. Our attack is performed in a
practical and unnoticeable query-based black-box manner with only a few nodes
on the graphs that can be accessed. Theoretical analysis and extensive
experiments demonstrate the effectiveness of our method by fooling the node
classifiers with only a small number of queries.
