  Graph Neural Networks (GNNs) have been shown to be effective models for
different predictive tasks on graph-structured data. Recent work on their
expressive power has focused on isomorphism tasks and countable feature spaces.
We extend this theoretical framework to include continuous features - which
occur regularly in real-world input domains and within the hidden layers of
GNNs - and we demonstrate the requirement for multiple aggregation functions in
this context. Accordingly, we propose Principal Neighbourhood Aggregation
(PNA), a novel architecture combining multiple aggregators with degree-scalers
(which generalize the sum aggregator). Finally, we compare the capacity of
different models to capture and exploit the graph structure via a novel
benchmark containing multiple tasks taken from classical graph theory,
alongside existing benchmarks from real-world domains, all of which demonstrate
the strength of our model. With this work, we hope to steer some of the GNN
research towards new aggregation methods which we believe are essential in the
search for powerful and robust models.
