  We study the convergence of message passing graph neural networks on random
graph models to their continuous counterpart as the number of nodes tends to
infinity. Until now, this convergence was only known for architectures with
aggregation functions in the form of normalized means, or, equivalently, of an
application of classical operators like the adjacency matrix or the graph
Laplacian. We extend such results to a large class of aggregation functions,
that encompasses all classically used message passing graph neural networks,
such as attention-based message passing, max convolutional message passing or
(degree-normalized) convolutional message passing. Under mild assumptions, we
give non-asymptotic bounds with high probability to quantify this convergence.
Our main result is based on the McDiarmid inequality. Interestingly, this
result does not apply to the case where the aggregation is a coordinate-wise
maximum. We treat this case separately and obtain a different convergence rate.
