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

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 us...

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Published inChinese physics B Vol. 25; no. 5; pp. 479 - 486
Main Author 焦波 聂原平 黄赪东 杜静 郭荣华 黄飞 石建迈
Format Journal Article
LanguageEnglish
Published 01.05.2016
Subjects
Evolution
Graphs
Mathematical models
Networks
Similarity
Spectra
Stability
Stability analysis
光谱特征
加权
无标度网络
树型
演化系统
稳定性分析
网络模型
谱分布
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/25/5/058901

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Summary: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 treelike 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.
Bibliography:weighted spectral distribution; pseudo tree-like model; deterministic network; scale-free and small-world network
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 treelike 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.
Bo Jiao, Yuan-ping Nie, Cheng-dong Huang, Jing Du, Rong-hua Guo, Fei Huang, and Jian-mai Shi（ 1Luoyang Electronic Equipment Test Center, Luoyang 471003, China 2 College of Computer, National University of Defense Technology, Changsha 410073, China 3 College of Information Systems and Management, National University of Defense Technology, Changsha 410073, China）
11-5639/O4
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SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/25/5/058901