  In reliable decision-making systems based on machine learning, models have to
be robust to distributional shifts or provide the uncertainty of their
predictions. In node-level problems of graph learning, distributional shifts
can be especially complex since the samples are interdependent. To evaluate the
performance of graph models, it is important to test them on diverse and
meaningful distributional shifts. However, most graph benchmarks considering
distributional shifts for node-level problems focus mainly on node features,
while structural properties are also essential for graph problems. In this
work, we propose a general approach for inducing diverse distributional shifts
based on graph structure. We use this approach to create data splits according
to several structural node properties: popularity, locality, and density. In
our experiments, we thoroughly evaluate the proposed distributional shifts and
show that they can be quite challenging for existing graph models. We also
reveal that simple models often outperform more sophisticated methods on the
considered structural shifts. Finally, our experiments provide evidence that
there is a trade-off between the quality of learned representations for the
base classification task under structural distributional shift and the ability
to separate the nodes from different distributions using these representations.
