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 | / 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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _2$$\end{document} shows an entirely different behavior than λ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _1$$\end{document}.
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