An insight into network structure measures and number of driver nodes

Control of complex networks is one of the most challenging open problems within network science. One view says that we can only claim to fully understand a network if we have the ability to influence or control it and predict the results of the employed control mechanisms. The area of control and controllability has progressed notably in the past ten years with several frameworks proposed namely, structural, exact, and physical. With continuing advancement in the area, the need to develop effective and efficient control methods that provide robust control is increasingly critical. The ultimate responsibility for controlling the network lies with the set of driver nodes that, according to the classical definition of the control theory of complex systems, can steer the network from any given state to a desired final state. To be able to develop better control mechanisms, we need to understand the relationship between different network structures and the number of driver nodes needed to control a given structure. This will allow understanding of which networks might be easier to control and the resources needed to control them. In this paper, we present a systematic study that builds an understanding of how network profiles (random (R), small-world (SW), scale-free (SF)) influence the number of driver nodes needed for control. Additionally, we also consider real social networks and identify their driver nodes set to further expand the discussion. We mean to find a correlation between network structure measures and number of driver nodes. Our results show that there is in fact a strong relationship between these.