Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence
Name
Preciado-2009-Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence.pdf
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982.64 KB
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Author(s)
Preciado, Victor M.
Verghese, George C.
Date Issued
August 2008
Journal
IEEE Transactions on Circuits and Systems I: Regular Papers
Publisher
Institute of Electrical and Electronics Engineers
Citation
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
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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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.
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DOI of Published Version
https://doi.org/10.1109/tcsi.2009.2023758
