A Graph Weighting Method for Reducing Consensus Time in Random Geographical Networks

Sensor networks are increasingly employed in many applications ranging from environmental to military cases. The network topology used in many sensor network applications has a kind of geographical structure. A graph weighting method for reducing consensus time in random geographical networks is proposed in this paper. We consider a method based on the mutually coupled oscillators for providing general consensus in the network. In this way, one can relate the consensus time to the properties of the Laplacian matrix of the connection graph, i.e. to the second smallest eigenvalue (algebraic connectivity). Our weighting algorithm is based on the node and edge between centrality measures. The proposed graph weighting method is in a way such that starting with a simple graph, i. e. an undirected and unweighted one; we end up with a directed and weighted graph. Our simulation results on sample geographical network show that this weighting is able to reduce the consensus time, and consequently the consensus cost. Reducing the consensus time have important role in reducing the energy consumption of the network, which is one of the most important concerns in designing and implementation of various types of sensor network solutions.