Individual dynamics induces symmetry in network controllability

Major advances have been made recently towards understanding how to control large networks by acting only on a small subset of their elements, illuminating the impact of a network’s topology on its controllability. Yet, a detailed understanding of the synergies between network topology and intrinsic individual dynamics is still lacking. Here we offer a theoretical framework to evaluate the controllability of complex networked systems with particular interest in the diversity of dynamic units characterized by different types of individual dynamics. Surprisingly, we find a universal symmetry accounting for the invariance of controllability with respect to exchanging the densities of any two different types of dynamic units, irrespective of the network topology. The highest controllability arises at the global symmetry point, at which different types of dynamic units have the same density. These findings have important implications for devising effective and sparse controllers of complex networked systems in a wide range of fields.