Controllability of complex networks based on propagation immunization

Control of complex network reflects humans' comprehension of complex system and the ability to reform it. Up-to-date research establishes the controllability theory of the complex networks based on linear system control theory. The theory could find a minimal set of driver nodes which controls all nodes' state in a linear time invariant complex network with any topology. However, this theory does not take into account the immune node or failure node which blocks the control signal. While inheriting the advantages of the theory, in the paper we first refine the complex network control model based on propagation immunization. Second we adopt four methods which belong to random immunization strategy and targeted immunization strategy to determine the immune nodes, and analyze the controllability of 14 real networks. The experimental results show that when the nodes which have higher degrees, betweeness or closeness are treated as immune nodes, the control of complex networks will become more difficult.