论文标题
真实和模型网络中的友谊悖论
The friendship paradox in real and model networks
论文作者
论文摘要
友谊悖论是观察到，任何网络中节点的邻居的程度平均将大于节点本身的程度。通常，您的朋友有比您更多的朋友。在本文中，我们发展了友谊悖论的数学理论，无论是通常的还是特定的模型网络，不仅集中在平均行为上，而且集中在平均值的变化上，并使用生成功能方法来计算利息量的完整分布。我们将理论的预测与对大量现实网络数据集的测量进行了比较，并发现了非常好的一致性。我们还为广义友谊悖论发展了同等的理论，该理论将节点以外的节点的特征与邻居的特征进行了比较。
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.
