Consensus dynamics in noisy trees with given parameters

In this paper, the leaderless coherence and leader-follower coherence defined by the Laplacian spectrum are applied to noisy trees with given parameters. The asymmetry of the trees is controlled by the degrees of hub nodes. Based on the tree's structures, analytical solutions are obtained for these two types of consensus algorithms. In order to compare the leaderless and leader-follower coherence, two trees with the same network size are selected and then explicit expressions of the coherence are given. Obtained results reveal that bigger difference of the degrees of the hubs leads to higher coherence and the consensus of a tree without a leader becomes better. Finally, it is found that the leader-follower coherence changes higher with more leaders and larger network parameters.