Controllability of complex networks aims to seek the lowest number of nodes (the driver nodes) that can control all the nodes by receiving the input signals. The concept of control centrality is used to determine the power of each node to control the network. The more a node controls the nodes through connections in the network, the more it has the power to control. Although the cooperative and free-rider strategies and the final level of cooperation in a population are considered and studied in the public goods game. However, it is yet to determine a solution to indicate the effectiveness of each member in changing the strategies of the other members. In a network, the choice of nodes effective in changing the other nodes’ strategies, as free-riders, will lead to lower cooperation and vice versa. This paper uses simulated and real networks to investigate that the nodes with the highest control power are more effective than the hubs, local, and random nodes in changing the strategies of the other nodes and the final level of cooperation. Results indicate that the nodes with the highest control power as free-riders, compared to the other sets being under consideration, can lead to a lower level of cooperation and are, therefore, more effective in changing the strategies of the other nodes. The obtained results can be considered in the treatment of cancer. So that, destroying the tumoral cells with the highest control power should be a priority as these cells have a higher capability to change the strategies of the other cells from cooperators to free-riders (healthy to tumoral).

Controllability of complex networks seeks the lowest number of nodes (driver nodes) that controlling all nodes by receiving input signals. The concept of control centrality is used to determine the power of each nodes in the control of the network. The more nodes a node controls through connections in the network, the more the power to control. In the public goods game, cooperative and free-rider strategies are considered and the final level of cooperation in a population is studied. However, it is yet to determine a solution for indicating the effectiveness of each member to change other member's strategies. In a network, the choice of nodes effective in changing other nodes strategy, as free-riders, will lead to lower cooperation and vice versa. This paper uses simulated and real networks to investigate the effectiveness of nodes with the highest control power in changing other nodes strategies and the final level of cooperation compared to the hubs, local, and random nodes. Results indicate that choosing the nodes with the highest control power as free-riders will lead to a lower level of cooperation and is, therefore, more effective in changing the strategies of other nodes, compared to other sets in consideration. This result can be considered in the treatment of cancer; with the explanation that, destroying tumoral cells with the highest control power should be a priority as these cells have a higher capability in changing the strategy of other cells from cooperators to free-riders (healthy to tumoral).