CONSENSUS ANALYSIS OF WEIGHTED GENERALIZED WINDMILL NETWORKS: BASED ON CENTRAL NODE IMPORTANCE SHIFT

In this paper, we analyze the consensus performance based on weighted generalized windmill networks with central node importance shift, where node importance is characterized by weighted degree centrality. Kooij proposed the generalized windmill graph. In this paper, we shift the weighted degree centrality of central nodes to marginal nodes, and remove partial ring structures of the generalized windmill graph. We derive analytical expressions of the first-order network coherence and convergence speed, which are quantified by Laplacian spectra. We find that besides shifting the weighted degree centrality of central nodes, removing partial ring structures also has a negative effect on the consensus performance. However, within a specific range of weight values, adjusting the weighting method has a positive effect on the consensus performance and can even offset the negative effect caused by removing partial ring structures.