Optimal leader selection for fast consensus via consensus centrality

In real applications, network resources are generally limited. Motivated by the significance of optimizing network, the consensus centrality index is proposed to quantify how fast a leader could guide all the nodes in a network to reach the desired consensus. On the basis of complex networks, the relation of the consensus centrality distribution and the degree distribution in several model and real networks is investigated. Moreover, the influence of network structure on consensus performance is studied. As the network becoming more heterogeneous or denser, the maximum consensus centrality increases. The faster convergence speed can be achieved if the node with the maximum consensus centrality is selected leader.