Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5384
Title: Markovian iterative method for degree distributions of growing networks
Authors: Shi, D
Zhou, H
Liu, L
Keywords: Complex networks
Iterative methods
Markov processes
Numerical analysis
Issue Date: Sep-2010
Publisher: American Physical Society
Source: Physical review E, statistical, nonlinear, and soft matter physics, Sept. 2010, v. 82, no. 3, 031105, p. 1-6 How to cite?
Journal: Physical review E, statistical, nonlinear, and soft matter physics 
Abstract: Currently, simulation is usually used to estimate network degree distribution P(k) and to examine if a network model predicts a scale-free network when an analytical formula does not exist. An alternative Markovian chain-based numerical method was proposed by Shi et al. Phys. Rev. E 71 036140 (2005) to compute time-dependent degree distribution P(k,t). Although the numerical results demonstrate a quick convergence of P(k,t) to P(k) for the Barabási-Albert model, the crucial issue on the rate of convergence has not been addressed formally. In this paper, we propose a simpler Markovian iterative method to compute P(k,t) for a class of growing network models. We also provide an upper bound estimation of the error of using P(k,t) to represent P(k) for sufficiently large t, and we show that with the iterative method, the rate of convergence of P(k,t) is root linear.
URI: http://hdl.handle.net/10397/5384
ISSN: 1539-3755 (print)
1550-2376 (online)
DOI: 10.1103/PhysRevE.82.031105
Rights: Physical Review E © 2010 The American Physical Society. The Journal's web site is located at http://pre.aps.org/
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