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Title: Markovian iterative method for degree distributions of growing networks
Authors: Shi, D
Zhou, H
Liu, L
Issue Date: Sep-2010
Source: Physical review. E, Statistical, nonlinear, and soft matter physics, Sept. 2010, v. 82, no. 3, 031105, p. 1-6
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.
Keywords: Complex networks
Iterative methods
Markov processes
Numerical analysis
Publisher: American Physical Society
Journal: Physical review. E, Statistical, nonlinear, and soft matter physics 
ISSN: 1539-3755
EISSN: 1550-2376
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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