Volume 99, Number 1, July 2012
|Number of page(s)||6|
|Published online||11 July 2012|
Exact eigenvalue spectrum of a class of fractal scale-free networks
1 School of Computer Science, Fudan University - Shanghai 200433, China
2 Shanghai Key Lab of Intelligent Information Processing, Fudan University - Shanghai 200433, China
3 School of Mathematical Sciences, Fudan University - Shanghai 200433, China
4 Department of Electronic Engineering, City University of Hong Kong - Hong Kong SAR, China
Received: 27 March 2012
Accepted: 15 June 2012
The eigenvalue spectrum of the transition matrix of a network encodes important information about its structural and dynamical properties. We study the transition matrix of a family of fractal scale-free networks and analytically determine all the eigenvalues and their degeneracies. We then use these eigenvalues to evaluate the closed-form solution to the eigentime for random walks on the networks under consideration. Through the connection between the spectrum of transition matrix and the number of spanning trees, we corroborate the obtained eigenvalues and their multiplicities.
PACS: 05.40.Fb – Random walks and Levy flights / 89.75.Hc – Networks and genealogical trees / 02.10.Yn – Matrix theory
© EPLA, 2012
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