Altering nodes types in controlling complex networks

Controlling a complex network towards a desired state is of great importance in many applications. A network can be controlled by inputting suitable external signals into some selected nodes, which are called driver nodes. Previous works found there exist two control modes in dense networks: distributed and centralized modes. For networks with the distributed mode, most of the nodes can be act as driver nodes; and those with the centralized mode, most of the nodes never be the driver nodes. Here we present an efficient algorithm to change the control type of nodes, from input nodes to redundant nodes, which is done by reversing edges of the network. We conclude four possible cases when reversing an edge and show the control mode can be changed by reversing very few in-edges of driver nodes. We evaluate the performance of our algorithm on both synthetic and real networks. The experimental results show that the control mode of a network can be easily changed by reversing a few elaborately selected edges, and the number of possible driver nodes is dramatically decreased. Our methods provide the ability to design the desired control modes of the network for different control scenarios, which may be used in many application regions.