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In this paper, an efficient approach to improve the connectivity of any given network is provided by introducing an additional node into the network. More specifically, the additional node acts as a neighbor to certain pair of nodes in the network with only changing one link among the existing nodes. The location of the additional node is designed according to the current topology as well as the states, and it has been proved that, controlling the most-connected node will in general improve the convergence rate of the network. Moreover, the proposed method overcomes the dependence of the convergence rate on the Fiedler value. In particular, the convergence problem is converted to a standard stability problem by using the cooperative control Lyapunov function, and a state-feedback controller with switching logic in finding the observed node is designed to guarantee the fast convergence. Simulation results demonstrate the effectiveness of the proposed strategy in speeding up consensus in a network.