  The ability to control complex networks is of crucial importance across a
wide range of applications in natural and engineering sciences. However, issues
of both theoretical and numerical nature introduce fundamental limitations to
controlling large-scale networks. In this paper, we cope with this problem by
introducing a coarse-graining algorithm. It leads to an aggregated network
which satisfies control equivalence, i.e., such that the optimal control values
for the original network can be exactly recovered from those of the aggregated
one. The algorithm is based on a partition refinement method originally devised
for systems of ordinary differential equations, here extended and applied to
linear dynamics on complex networks. Using a number of benchmarks from the
literature we show considerable reductions across a variety of networks from
biology, ecology, engineering, and social sciences.
