Graph Neural Networks (GNNs) are a wide class of connectionist models for
graph processing. They perform an iterative message passing operation on each
node and its neighbors, to solve classification/ clustering tasks -- on some
nodes or on the whole graph -- collecting all such messages, regardless of
their order. Despite the differences among the various models belonging to this
class, most of them adopt the same computation scheme, based on a local
aggregation mechanism and, intuitively, the local computation framework is
mainly responsible for the expressive power of GNNs. In this paper, we prove
that the Weisfeiler--Lehman test induces an equivalence relationship on the
graph nodes that exactly corresponds to the unfolding equivalence, defined on
the original GNN model. Therefore, the results on the expressive power of the
original GNNs can be extended to general GNNs which, under mild conditions, can
be proved capable of approximating, in probability and up to any precision, any
function on graphs that respects the unfolding equivalence.Comment: 16 pages, 3 figure