标题： 初始网络配置对优先连接的影响 显示英文标题

标题： The effect of the initial network configuration on preferential attachment

摘要： 经典的偏好连接模型对网络初始配置的选择非常敏感。随着初始节点数量及其度的增长，达到平衡度分布所需的时间也随之增加。我们研究了这一现象，提供了平衡时间的估计，并描述了在有限时间内观察到的度分布截断。当初始网络密集且超过某个小尺寸时，不会达到平衡状态，且适当的统计检验总能区分生成的度分布与平衡度分布。作为副产品，当数据充足时，加权的科尔莫戈罗夫-斯米尔诺夫统计量被证明更适合分析具有截断的幂律分布的统计特性。 显示英文摘要

摘要： The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be established. We study this phenomenon, provide estimates of the equilibration time, and characterize the degree distribution cutoff observed at finite times. When the initial network is dense and exceeds a certain small size, there is no equilibration and a suitable statistical test can always discern the produced degree distribution from the equilibrium one. As a by-product, the weighted Kolmogorov-Smirnov statistic is demonstrated to be more suitable for statistical analysis of power-law distributions with cutoff when the data is ample.