复制模型及其度分布的统计规律

基于复制机制在网络增长中的重要性,通过计算机对完全复制模型和部分复制模型做了大量的模拟,并采用经验统计的方法对庞大的计算机模拟数据做统计分析,来研究两种复制模型入度的结点度分布、扰动和发散规律,结果显示:两种复制模型的入度分别服从衰减指数γ=2和γ=3.5(p=0.5)的幂律分布,且入度分布完全独立于演化时间或网络规模;两种模型的小度结点个数都服从正态分布;完全复制模型的最大入度不具有随机性,而部分复制模型的最大度数服从对数正态分布;给出了最大度关于时间t的一个经验公式Ekm(t)]～Cp.t。

Statistical law of the in-degree about copying model

Based on the importance of copying mechanism for growing networks,we did extensive simulations about fully copying model and partially copying model,and we adopted the experience statistic method to analyse large amounts of data in order to study in-degree distributions,divergence forms and fluctuation laws of the in-degree about copying models.Firstly,the result showed that in-degree distributions about two kinds of models obey power-law with γ=2 and γ=3.5(p=0.5) respectively and they are independent of evolution time or network size.Secondly,the number of small degree nodes with k=5 obeys normal distribution.Thirdly,the maximum degree about fully copying model does not have any randomness,however,the maximum degree about partially copying model obeys log-normal distribution.Finally,an experiential formula between the maximum degree and evolution time was given.