  This paper studies Dropout Graph Neural Networks (DropGNNs), a new approach
that aims to overcome the limitations of standard GNN frameworks. In DropGNNs,
we execute multiple runs of a GNN on the input graph, with some of the nodes
randomly and independently dropped in each of these runs. Then, we combine the
results of these runs to obtain the final result. We prove that DropGNNs can
distinguish various graph neighborhoods that cannot be separated by message
passing GNNs. We derive theoretical bounds for the number of runs required to
ensure a reliable distribution of dropouts, and we prove several properties
regarding the expressive capabilities and limits of DropGNNs. We experimentally
validate our theoretical findings on expressiveness. Furthermore, we show that
DropGNNs perform competitively on established GNN benchmarks.
