Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence
We study the eigenvalue distribution of the Kirchhoff matrix of a large-scale probabilistic network with a prescribed expected degree sequence. This spectrum plays a key role in many dynamical and structural network problems such as synchronization of a network of oscillators. We introduce analytica...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/60051 https://orcid.org/0000-0002-5930-7694 |
| _version_ | 1811080789221179392 |
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| author | Preciado, Victor M. Verghese, George C. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Preciado, Victor M. Verghese, George C. |
| author_sort | Preciado, Victor M. |
| collection | MIT |
| description | We study the eigenvalue distribution of the Kirchhoff matrix of a large-scale probabilistic network with a prescribed expected degree sequence. This spectrum plays a key role in many dynamical and structural network problems such as synchronization of a network of oscillators. We introduce analytical expressions for the first three moments of the eigenvalue distribution of the Kirchhoff matrix, as well as a probabilistic asymptotic analysis of these moments for a graph with a prescribed expected degree sequence. These results are applied to the analysis of synchronization in a large-scale probabilistic network of oscillators. |
| first_indexed | 2024-09-23T11:36:52Z |
| format | Article |
| id | mit-1721.1/60051 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:36:52Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/600512022-09-27T20:43:34Z Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence Preciado, Victor M. Verghese, George C. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Verghese, George C. Verghese, George C. We study the eigenvalue distribution of the Kirchhoff matrix of a large-scale probabilistic network with a prescribed expected degree sequence. This spectrum plays a key role in many dynamical and structural network problems such as synchronization of a network of oscillators. We introduce analytical expressions for the first three moments of the eigenvalue distribution of the Kirchhoff matrix, as well as a probabilistic asymptotic analysis of these moments for a graph with a prescribed expected degree sequence. These results are applied to the analysis of synchronization in a large-scale probabilistic network of oscillators. 2010-12-02T14:01:12Z 2010-12-02T14:01:12Z 2008-08 2009-06 Article http://purl.org/eprint/type/JournalArticle 1549-8328 INSPEC Accession Number: 10729851 http://hdl.handle.net/1721.1/60051 Preciado, V.M., and G.C. Verghese. “Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence.” Circuits and Systems I: Regular Papers, IEEE Transactions on 56.6 (2009): 1231-1240. © Copyright 2010 IEEE https://orcid.org/0000-0002-5930-7694 en_US http://dx.doi.org/10.1109/tcsi.2009.2023758 IEEE Transactions on Circuits and Systems I: Regular Papers Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Preciado, Victor M. Verghese, George C. Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title | Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title_full | Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title_fullStr | Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title_full_unstemmed | Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title_short | Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence |
| title_sort | low order spectral analysis of the kirchhoff matrix for a probabilistic graph with a prescribed expected degree sequence |
| url | http://hdl.handle.net/1721.1/60051 https://orcid.org/0000-0002-5930-7694 |
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