arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2012.03991cs.SIphysics.soc-ph
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真实网络和模型网络中的友谊悖论

The friendship paradox in real and model networks

George T. Cantwell, Alec Kirkley, M. E. J. Newman

摘要:

友谊悖论是一种观察,即在任何网络中,节点邻居的度平均来说都大于节点本身的度。用通俗的话说,你的朋友比你有更多的朋友。在本文中,我们发展了友谊悖论的数学理论,无论是在一般情况下,以及特定的模型网络,不仅关注平均行为,而且对平均值的变化,并使用生成函数的方法来计算感兴趣的数量的全分布。我们将我们的理论预测与大量真实网络数据集的测量结果进行了比较,发现非常吻合。我们还开发了等价的理论,广义的友谊悖论,比较节点的特性,而不是程度,他们的邻居。

英文摘要:

The friendship paradox is the observation that the degrees of the neighbors of a node in any network will, on average, be greater than the degree of the node itself. In common parlance, your friends have more friends than you do. In this paper we develop the mathematical theory of the friendship paradox, both in general as well as for specific model networks, focusing not only on average behavior but also on variation about the average and using generating function methods to calculate full distributions of quantities of interest. We compare the predictions of our theory with measurements on a large number of real-world network data sets and find remarkably good agreement. We also develop equivalent theory for the generalized friendship paradox, which compares characteristics of nodes other than degree to those of their neighbors.

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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