  Graph Neural Networks (GNNs) rely on the graph structure to define an
aggregation strategy where each node updates its representation by combining
information from its neighbours. A known limitation of GNNs is that, as the
number of layers increases, information gets smoothed and squashed and node
embeddings become indistinguishable, negatively affecting performance.
Therefore, practical GNN models employ few layers and only leverage the graph
structure in terms of limited, small neighbourhoods around each node.
Inevitably, practical GNNs do not capture information depending on the global
structure of the graph. While there have been several works studying the
limitations and expressivity of GNNs, the question of whether practical
applications on graph structured data require global structural knowledge or
not, remains unanswered. In this work, we empirically address this question by
giving access to global information to several GNN models, and observing the
impact it has on downstream performance. Our results show that global
information can in fact provide significant benefits for common graph-related
tasks. We further identify a novel regularization strategy that leads to an
average accuracy improvement of more than 5% on all considered tasks.
