Exact calculations of network coherence in weighted ring-trees networks and recursive trees

Abstract

In this paper, we study noisy consensus dynamics in two families of weighted ring-trees networks and recursive trees with a controlled initial state. Based on the topological structures, we obtain exact expressions for the first- and second-order network coherence as a function of the involved parameters and provide the scalings of network coherence regarding network size. We then show that the weights dominate the consensus behaviors and the scalings. Finally, we make a comparison of the network coherence between the ring-trees networks and the recursive trees with the same number of nodes and show that the consensus of ring-trees networks is better than the trees since the initial state in the ring-trees networks is a ring.