NETWORK COHERENCE ANALYSIS ON A FAMILY OF NESTED WEIGHTED n-POLYGON NETWORKS

In this paper, we propose a family of nested weighted n-polygon networks, which is a kind of promotion of infinite fractal dimension networks. We study the coherence of the networks with recursive features that contain the initial states dominated by a weighted parameter. The network coherence is a consensus problem with additive noises, and it is known that coherence is defined by the eigenvalues of the Laplacian matrix. According to the structure of recursive nested model, we get the recursive expressions of Laplacian eigenvalues and further derive the exact results of first- and second-order coherence. Finally, we investigate the influential impacts on the coherence for different large parameters and discuss the relationship between Laplacian energy and network coherence. Furthermore, we obtain the expressions of Kirchhoff index, mean first-passage time and average path length of the networks.

Automated summary

This paper proposes a family of nested weighted n-polygon networks, studies the coherence of networks with recursive features, and investigates the influential impacts on coherence for different large parameters. By deriving recursive expressions of Laplacian eigenvalues, the exact results of first- and second-order coherence are obtained, and the relationship between Laplacian energy and network coherence is discussed. Additionally, expressions of Kirchhoff index, mean first-passage time, and average path length of the networks are derived.