On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum

On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum

In this paper, we mainly study the performance of star-composed networks which can achieve consensus. Specifically, we investigate the convergence speed and robustness of the consensus of the networks, which can be measured by the smallest nonzero eigenvalue λ2 of the Laplacian matrix and the H2 nor...

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Main Authors: Da Huang, Haijun Jiang, Zhiyong Yu, Qiongxiang Huang, Xing Chen
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/4619514
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spelling doaj-32b0fb04722e4d1689ced46a6702006f2020-11-24T22:44:34ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/46195144619514On Consensus of Star-Composed Networks with an Application of Laplacian SpectrumDa Huang0Haijun Jiang1Zhiyong Yu2Qiongxiang Huang3Xing Chen4College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaXinjiang Institute of Engineering, Urumqi, Xinjiang 830023, ChinaIn this paper, we mainly study the performance of star-composed networks which can achieve consensus. Specifically, we investigate the convergence speed and robustness of the consensus of the networks, which can be measured by the smallest nonzero eigenvalue λ2 of the Laplacian matrix and the H2 norm of the graph, respectively. In particular, we introduce the notion of the corona of two graphs to construct star-composed networks and apply the Laplacian spectrum to discuss the convergence speed and robustness for the communication network. Finally, the performances of the star-composed networks have been compared, and we find that the network in which the centers construct a balanced complete bipartite graph has the most advantages of performance. Our research would provide a new insight into the combination between the field of consensus study and the theory of graph spectra.http://dx.doi.org/10.1155/2017/4619514
collection DOAJ
language English
format Article
sources DOAJ
author Da Huang
Haijun Jiang
Zhiyong Yu
Qiongxiang Huang
Xing Chen
spellingShingle Da Huang
Haijun Jiang
Zhiyong Yu
Qiongxiang Huang
Xing Chen
On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
Discrete Dynamics in Nature and Society
author_facet Da Huang
Haijun Jiang
Zhiyong Yu
Qiongxiang Huang
Xing Chen
author_sort Da Huang
title On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
title_short On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
title_full On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
title_fullStr On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
title_full_unstemmed On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum
title_sort on consensus of star-composed networks with an application of laplacian spectrum
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2017-01-01
description In this paper, we mainly study the performance of star-composed networks which can achieve consensus. Specifically, we investigate the convergence speed and robustness of the consensus of the networks, which can be measured by the smallest nonzero eigenvalue λ2 of the Laplacian matrix and the H2 norm of the graph, respectively. In particular, we introduce the notion of the corona of two graphs to construct star-composed networks and apply the Laplacian spectrum to discuss the convergence speed and robustness for the communication network. Finally, the performances of the star-composed networks have been compared, and we find that the network in which the centers construct a balanced complete bipartite graph has the most advantages of performance. Our research would provide a new insight into the combination between the field of consensus study and the theory of graph spectra.
url http://dx.doi.org/10.1155/2017/4619514
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AT haijunjiang onconsensusofstarcomposednetworkswithanapplicationoflaplacianspectrum
AT zhiyongyu onconsensusofstarcomposednetworkswithanapplicationoflaplacianspectrum
AT qiongxianghuang onconsensusofstarcomposednetworkswithanapplicationoflaplacianspectrum
AT xingchen onconsensusofstarcomposednetworkswithanapplicationoflaplacianspectrum
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