Noisy consensus dynamics in windmill-type graphs

In the present study, two types of consensus algorithms, including the leaderless coherence and the leader–follower coherence quantified by the Laplacian spectrum, are applied to noisy windmill graphs. Based on the graph construction, exact solutions are obtained for the leader–follower coherence with freely assigned leaders. In order to compare consensus dynamics of two nonisomorphic graphs with the same number of nodes and edges, two generalized windmill graphs are selected as the network models and then explicit expressions of the network coherence are obtained. Then, coherences of models are compared. The obtained results reveal distinct coherence behaviors originating from intrinsic structures of models. Finally, the robustness of the coherence is analyzed. Accordingly, it is found that graph parameters and the number of leaders have a profound impact on the studied consensus algorithms.