Stability of weighted spectral distribution in a pseudo tree-like network model

doi:10.1088/1674-1056/25/5/058901

Abstract

The comparison of networks with different orders strongly depends on the stability analysis of graph features in evolving systems. In this paper, we rigorously investigate the stability of the weighted spectral distribution (i.e., a spectral graph feature) as the network order increases. First, we use deterministic scale-free networks generated by a pseudo tree-like model to derive the precise formula of the spectral feature, and then analyze the stability of the spectral feature based on the precise formula. Except for the scale-free feature, the pseudo tree-like model exhibits the hierarchical and small-world structures of complex networks. The stability analysis is useful for the classification of networks with different orders and the similarity analysis of networks that may belong to the same evolving system.

Keywords: weighted spectral distribution pseudo tree-like model deterministic network scale-free and small-world network

Received: 23 September 2015
Revised: 26 December 2015
Accepted manuscript online:

PACS:	89.75.Hc	(Networks and genealogical trees)
	05.40.Fb	(Random walks and Levy flights)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)

Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 61402485, 61303061, and 71201169).

Corresponding Authors: Bo Jiao
E-mail: jiaoboleetc@outlook.com

Cite this article:

Bo Jiao(焦波), Yuan-ping Nie(聂原平), Cheng-dong Huang(黄赪东), Jing Du(杜静), Rong-hua Guo(郭荣华), Fei Huang(黄飞), Jian-mai Shi(石建迈) Stability of weighted spectral distribution in a pseudo tree-like network model 2016 Chin. Phys. B 25 058901

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[1]	Scaling of weighted spectral distribution in weighted small-world networks Bo Jiao(焦波), Xiao-Qun Wu(吴晓群). Chin. Phys. B, 2017, 26(2): 028901.

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