  Graph neural networks compute node representations by performing multiple
message-passing steps that consist in local aggregations of node features.
Having deep models that can leverage longer-range interactions between nodes is
hindered by the issues of over-smoothing and over-squashing. In particular, the
latter is attributed to the graph topology which guides the message-passing,
causing a node representation to become insensitive to information contained at
distant nodes. Many graph rewiring methods have been proposed to remedy or
mitigate this problem. However, properly evaluating the benefits of these
methods is made difficult by the coupling of over-squashing with other issues
strictly related to model training, such as vanishing gradients. Therefore, we
propose an evaluation setting based on message-passing models that do not
require training to compute node and graph representations. We perform a
systematic experimental comparison on real-world node and graph classification
tasks, showing that rewiring the underlying graph rarely does confer a
practical benefit for message-passing.
