On the fiedler vector of graphs and its application in consensus networks

In this paper, we examine the influence of the normalized eigenvectors of the graph Laplacian matrix on the behavior of individual agents undergoing consensus dynamics. We show that the Fielder vector can be estimated from the states of the agents and that the entries of this vector can describe the subsequent behavior of the agents. In addition, we discuss how the Fiedler vector sheds light on the energy damping rate of the consensus network driven by unit impulse. As an application, we show that the characteristic set of a graph can be identified based on the corresponding Fiedler vector.