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

Jia-Bao Liu, Yan Bao, Wu-Ting Zheng () and Sakander Hayat ()
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Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China
Yan Bao: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China
Wu-Ting Zheng: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, P. R. China
Sakander Hayat: Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi Swabi, Khyber Pakhtunkhwa, Pakistan

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-15

Abstract: 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.

Keywords: Fractal Networks; Network Coherence; Consensus (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (7)

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DOI: 10.1142/S0218348X21502601

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