### Abstract

Original language | English |
---|---|

Pages (from-to) | 031105 |

Journal | Physical Review E |

Volume | 82 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2 Sep 2010 |

Externally published | Yes |

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### Cite this

*Physical Review E*,

*82*(3), 031105. https://doi.org/10.1103/PhysRevE.82.031105

}

*Physical Review E*, vol. 82, no. 3, pp. 031105. https://doi.org/10.1103/PhysRevE.82.031105

**Markovian iterative method for degree distributions of growing networks.** / SHI, Dinghua; ZHOU, Huijie; LIU, Liming.

Research output: Journal Publications › Journal Article (refereed)

TY - JOUR

T1 - Markovian iterative method for degree distributions of growing networks

AU - SHI, Dinghua

AU - ZHOU, Huijie

AU - LIU, Liming

PY - 2010/9/2

Y1 - 2010/9/2

N2 - 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 Barabasi-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.

AB - 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 Barabasi-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.

UR - http://commons.ln.edu.hk/sw_master/159

U2 - 10.1103/PhysRevE.82.031105

DO - 10.1103/PhysRevE.82.031105

M3 - Journal Article (refereed)

C2 - 21230023

VL - 82

SP - 031105

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 3

ER -