  Graph Neural Networks (GNNs) extend the success of neural networks to
graph-structured data by accounting for their intrinsic geometry. While
extensive research has been done on developing GNN models with superior
performance according to a collection of graph representation learning
benchmarks, it is currently not well understood what aspects of a given model
are probed by them. For example, to what extent do they test the ability of a
model to leverage graph structure vs. node features? Here, we develop a
principled approach to taxonomize benchmarking datasets according to a
$\textit{sensitivity profile}$ that is based on how much GNN performance
changes due to a collection of graph perturbations. Our data-driven analysis
provides a deeper understanding of which benchmarking data characteristics are
leveraged by GNNs. Consequently, our taxonomy can aid in selection and
development of adequate graph benchmarks, and better informed evaluation of
future GNN methods. Finally, our approach and implementation in
$\texttt{GTaxoGym}$ package are extendable to multiple graph prediction task
types and future datasets.
