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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/4619514 |
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| _version_ | 1832560857081446400 |
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| author | Da Huang Haijun Jiang Zhiyong Yu Qiongxiang Huang Xing Chen |
| author_facet | Da Huang Haijun Jiang Zhiyong Yu Qiongxiang Huang Xing Chen |
| author_sort | Da Huang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-32b0fb04722e4d1689ced46a6702006f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-32b0fb04722e4d1689ced46a6702006f2025-02-03T01:26:35ZengWileyDiscrete 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2017/4619514 |
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