On the controllability of isotropic and anisotropic networks

This paper studies the controllability degree of complex networks as a function of the network weights and the location and number of control nodes. We quantify the controllability degree of a network with the worst-case control energy to drive the network to an arbitrary configuration. We show that isotropic networks are difficult to control, as the control energy grows exponentially with the network cardinality when the number of control nodes remains constant. Conversely, we prove that sufficiently anisotropic networks are easy to control, as the control energy is bounded independently of the network cardinality and number of control nodes.