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A model for collaboration networks giving rise to a power law distribution with exponential cutoff

机译:一种协作网络模型,该模型产生幂律分布且具有指数截止

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摘要

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get richer'' phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein, e-mail, actor and collaboration networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will become inactive. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model empirically by analysing the Mathematical Research collaboration network, the distribution of which is known to follow a power law with an exponential cutoff.
机译:最近,有几位作者提出了用于复杂网络增长的随机进化模型,这些模型导致了幂律分布。这些模型基于优先依恋的概念,导致``富人越富''现象。尽管建议的随机模型具有一般性,但仍然存在一些无法解释的现象,这可能是由于蛋白质,电子邮件,参与者和协作网络等网络规模有限所致。实际上,这样的网络可能在幂律定标中表现出指数截止,尽管对于大型网络而言,只有在分布的尾部才可以观察到该截止。我们建议对基本随机演化模型进行修改,以便在优先选择节点后(例如,根据其内联节点的数量),该节点变为非活动状态的可能性很小。我们表明,作为此修改的结果,通过查看传递模型的随机过程,我们获得了具有指数截止值的幂律分布。与许多其他模型不同,当前模型可以捕获分布的指数小于或等于2的实例。作为概念的证明,我们通过分析数学研究协作网络以经验方式证明模型的一致性,已知该协作网络的分布遵循幂幂定律,并且具有指数截止值。

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