de Blasio Birgitte Freiesleben, Seierstad Taral Guldahl, Aalen Odd O
University of Oslo Norway.
J R Stat Soc Ser C Appl Stat. 2011 Mar;60(2):239-259. doi: 10.1111/j.1467-9876.2010.00746.x.
Preferential attachment is a proportionate growth process in networks, where nodes receive new links in proportion to their current degree. Preferential attachment is a popular generative mechanism to explain the widespread observation of power-law-distributed networks. An alternative explanation for the phenomenon is a randomly grown network with large individual variation in growth rates among the nodes (frailty). We derive analytically the distribution of individual rates, which will reproduce the connectivity distribution that is obtained from a general preferential attachment process (Yule process), and the structural differences between the two types of graphs are examined by simulations. We present a statistical test to distinguish the two generative mechanisms from each other and we apply the test to both simulated data and two real data sets of scientific citation and sexual partner networks. The findings from the latter analyses argue for frailty effects as an important mechanism underlying the dynamics of complex networks.
偏好依附是网络中的一种按比例增长的过程，其中节点接收新链接的比例与其当前的度成正比。偏好依附是一种流行的生成机制，用于解释幂律分布网络的广泛观测现象。对该现象的另一种解释是一个随机增长的网络，其中节点之间的增长率存在较大的个体差异（脆弱性）。我们通过分析得出个体增长率的分布，该分布将重现从一般偏好依附过程（尤尔过程）中获得的连通性分布，并通过模拟研究这两种类型图之间的结构差异。我们提出了一种统计检验来区分这两种生成机制，并将该检验应用于模拟数据以及科学引文和性伴侣网络的两个真实数据集。后一种分析的结果表明，脆弱性效应是复杂网络动态背后的一个重要机制。
