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.

在本文中，我们研究了两类加权环树网络和具有受控初始状态的递归树中的嘈杂共识动态。基于拓扑结构，我们获得了作为所涉及参数的函数的一阶和二阶网络相干性的精确表达式，并提供了关于网络大小的网络相干性的标度。然后我们表明权重主导了共识行为和缩放。最后，我们对环树网络和具有相同节点数的递归树之间的网络一致性进行了比较，并表明环树网络的一致性优于环树中初始状态以来的树网络是一个环。