Dominating scale-free networks with variable scaling exponent: heterogeneous networks are not difficult to control

The possibility of controlling and directing a complex system's behavior at will is rooted in its interconnectivity and can lead to significant advances in disparate fields, ranging from nationwide energy saving to therapies that involve multiple targets. In this work, we address complex network controllability from the perspective of the minimum dominating set (MDS). Our theoretical calculations, simulations using artificially generated networks as well as real-world network analyses show that the more heterogeneous a network degree distribution is, the easier it is to control the entire system. We demonstrate that relatively few nodes are needed to control the entire network if the power-law degree exponent is smaller than 2, whereas many nodes are required if it is larger than 2.