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arXiv 1408.6596physics.soc-phcond-mat.stat-mechcs.SIphysics.data-an
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无同质性熟人模型中聚类的出现

Emergence of Clustering in an Acquaintance Model without Homophily

Uttam Bhat, P. L. Krapivsky, S. Redner

摘要:

我们引入了一个基于代理的熟人模型,其中社会联系的过程中,没有明确的同质性。尽管社会互动具有同质性,但高度聚集的社交网络可能会出现。我们的模型的关键特征是变量传递相互作用。也就是说,当一个代理人介绍两个没有联系的朋友时,他们之间实际发生联系的速度取决于他们共同认识的人的数量。随着这种传递性交互率的变化,社会网络经历了一个戏剧性的聚类过渡。在接近过渡期时,网络由一系列定义明确的社区组成。作为时间的函数,网络也可以经历\emph{incomplete}凝胶化转变,其中凝胶或巨簇即使在无限时间也不构成整个网络。我们模型的一些聚类特性也出现了,但在Facebook网络中是以一种更渐进的方式出现的。最后,我们讨论了一个更现实的变体,我们的原始模型中,有一个软截止率的传递相互作用。有了这个变体,人们可以构建与Facebook网络定量匹配的网络实现。

英文摘要:

We introduce an agent-based acquaintance model in which social links are created by processes in which there is no explicit homophily. In spite of the homogeneous nature of the social interactions, highly-clustered social networks can arise. The crucial feature of our model is that of variable transitive interactions. Namely, when an agent introduces two unconnected friends, the rate at which a connection actually occurs between them depends on the number of their mutual acquaintances. As this transitive interaction rate is varied, the social network undergoes a dramatic clustering transition. Close to the transition, the network consists of a collection of well-defined communities. As a function of time, the network can also undergo an \emph{incomplete} gelation transition, in which the gel, or giant cluster, does not constitute the entire network, even at infinite time. Some of the clustering properties of our model also arise, but in a more gradual manner, in Facebook networks. Finally, we discuss a more realistic variant of our original model in which there is a soft cutoff in the rate of transitive interactions. With this variant, one can construct network realizations that quantitatively match Facebook networks.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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