Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence
Author(s)
Preciado, Victor M.; Verghese, George C.
DownloadPreciado-2009-Low-Order Spectral Analysis of the Kirchhoff Matrix for a Probabilistic Graph With a Prescribed Expected Degree Sequence.pdf (982.6Kb)
PUBLISHER_POLICY
Publisher Policy
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.
Terms of use
Metadata
Show full item recordAbstract
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.
Date issued
2008-08Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer ScienceJournal
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
Other identifiers
INSPEC Accession Number: 10729851
ISSN
1549-8328