LEADER–FOLLOWER COHERENCE OF THE WEIGHTED RECURSIVE TREE NETWORKS

Recently, the consensus problem has attracted extensive attention of researchers from different scientific communities. In this paper, we study the leader–follower network coherence (i.e. the mean steady-state variance of the deviation from the static value of the leader nodes) in the weighted recursive tree networks with assigning the leaders orderly in the initial state. For the weighted recursive tree networks model, we study the characteristic polynomial of the Laplacian submatrix and obtain the relationship for the eigenvalues in two successive generations. The analytical formula of the leader–follower network coherence related by the sum of the reciprocal of all eigenvalues of this submatrix is obtained. The result shows that more number of leaders and the greater weight factor lead to better consensus.