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arXiv physics/0607188physics.soc-ph
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社交网络的随机演化增长模型

A Stochastic Evolutionary Growth Model for Social Networks

Trevor Fenner, Mark Levene, George Loizou, George Roussos

摘要:

我们提出了一个随机模型的社会网络,新的演员可能会加入网络,现有的演员可能会变得不活跃,并在稍后的阶段,重新激活自己。我们的模型捕捉网络的演变,假设演员获得新的关系或根据优先连接规则变得活跃。我们推导出这个随机模型的平均场方程,并表明,渐近,演员的分布服从幂律分布。特别地,该模型适用于社交网络,例如无线局域网,其中用户连接到接入点,以及对等网络,其中用户彼此连接。作为一个概念的证明,我们证明了我们的模型的有效性,经验分析一个公共日志包含在达特茅斯学院的无线网络的痕迹在一段时间内的三年。分析数据处理,根据我们的模型,我们证明了用户访问的分布是渐近的幂律分布。

英文摘要:

We present a stochastic model for a social network, where new actors may join the network, existing actors may become inactive and, at a later stage, reactivate themselves. Our model captures the evolution of the network, assuming that actors attain new relations or become active according to the preferential attachment rule. We derive the mean-field equations for this stochastic model and show that, asymptotically, the distribution of actors obeys a power-law distribution. In particular, the model applies to social networks such as wireless local area networks, where users connect to access-points, and peer-to-peer networks where users connect to each other. As a proof of concept, we demonstrate the validity of our model empirically by analysing a public log containing traces from a wireless network at Dartmouth College over a period of three years. Analysing the data processed according to our model, we demonstrate that the distribution of user accesses is asymptotically a power-law distribution.

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