Markovian iterative method for degree distributions of growing networks

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 [Phys. Rev. E 71, 036140 (2005)]10.1103/PhysRevE.71.036140 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. © 2010 The American Physical Society.