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On the second largest eigenvalue of networks
被引:0
作者:
Ankit Mishra
Ranveer Singh
Sarika Jalan
机构:
[1] Indian Institute of Technology Indore,Department of Physics
[2] Indian Institute of Technology Indore,Computer science and Engineering
来源:
Applied Network Science
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7卷
关键词:
Networks;
Spectra;
D O I:
暂无
中图分类号:
学科分类号:
摘要:
From predicting the epidemic threshold of a disease outbreak to anticipating the stability of a complex system, analysis of spectra of the adjacency matrices of the underlying networks play a pivotal role. Despite spectra of networks considered as fingerprints of the corresponding complex systems, most works and review articles have circumscribed around the largest eigenvalue (λ1\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _1$$\end{document}) only. The second largest eigenvalue of a network that admits many applications in diverse fields, including mathematics and computer science, has not been thoroughly contemplated. This article first reviews existing literature on λ2\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _2$$\end{document}, predominantly confined to the random regular graphs, followed by the results for various popular model networks. We emphasize the aspect that λ2\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _2$$\end{document} shows an entirely different behavior than λ1\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _1$$\end{document}.
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