  In this paper, we propose a new method to compute the barycenter of large
weighted graphs endowed with probability measures on their nodes. We suppose
that the edge weights are distances between the nodes and that the probability
measure on the nodes is related to events observed there. For instance, a graph
can represent a subway network: its edge weights are the distance between two
stations, and the observed events at each node are the subway users getting in
or leaving the subway network at this station. The probability measure on the
nodes does not need to be explicitly known. Our strategy only uses observed
node related events to give more or less emphasis to the different nodes.
Furthermore, the barycenter estimation can be updated in real time with each
new event.
  We propose a multiscale extension of \cite{arXiv:1605.04148} where the
decribed strategy is valid only for medium-sized graphs due to memory costs.
Our multiscale approach is inspired from the geometrical decomposition of the
barycenter in a Euclidean space: we apply a heuristic \textit{divide et impera}
strategy based on a preliminary clustering. Our strategy is finally assessed on
road- and social-networks of up to $10^6$ nodes. We show that its results
compare well with \cite{arXiv:1605.04148} in terms of accuracy and stability on
small graphs, and that it can additionally be used on large graphs even on
standard laptops.
