Degree of relative influence for consensus-type networks

In this work, a novel metric is introduced in order to measure the influence of one subgroup of agents on another in consensus-type networks. The measure is solely graph-depended and its value can be calculated from the normalized eigenvector corresponding to the second smallest eigenvalue of graph Laplacian, known as the Fiedler vector and widely used in graph partitioning algorithms. We also examine this metric for the influenced consensus model where external agents could attach to the network in order to influence the evolution of the agents´ states. It is shown that the proposed metric is similar to a network centrality measure, capable of quantifying the effectiveness of the network attachment. As such, leader selection scenario is subsequently investigated via this metric.