Weighted coupling for geographical networks: Application to reducing consensus time in sensor networks

Although many complex real-world networks are weighted, unweighted networks are used in many applications such as sensor networks. In this Letter it is shown using properly weighted networks the performance can be greatly enhanced by reducing the time necessary for the average consensus. Random geographical models are adapted as network models and a method based on mutually coupled phase oscillators is used for providing average consensus over the network. The consensus time is calculated by numerically solving the network's differential equations and monitoring the average error. The simulation results on some sample networks show that the consensus time is dramatically reduced when the proposed weights are used for the links of the underlying network.