  Symmetries are an essential feature of complex networks as they regulate how
the graph collective dynamics organizes into clustered states. We here show how
to control network symmetries, and how to enforce patterned states of
synchronization with nodes clustered in a desired way. Our approach consists of
perturbing the original network connectivity, either by adding new edges or by
adding/removing links together with modifying their weights. By solving
suitable optimization problems, we furthermore guarantee that changes made on
the existing topology are minimal. The conditions for the stability of the
enforced pattern are derived for the general case, and the performance of the
method is illustrated with paradigmatic examples. Our results are relevant to
all the practical situations in which coordination of the networked systems
into diverse groups may be desirable, such as for teams of robots, unmanned
autonomous vehicles, power grids and central pattern generators.
