We consider a friendship model in which each member of a community has a latent value such that the probability that any two individuals are friends is a function of their latent values. We consider such questions as does information that i and j are both friends with k make it more likely that i and j are themselves friends. Among other things, we show that for fixed sets S and T, the more friends that i has in S, then the stochastically more friends i has in T. We consider how a variation of the friendship paradox applies to our model. We also study the distribution of the number of friendless individuals in the community and derive a bound on the total variation distance between it and a Poisson with the same mean.

中文翻译：

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概率友谊网络模型

我们考虑一个友谊模型，其中社区的每个成员都有一个潜在价值，因此任何两个人成为朋友的概率是他们潜在价值的函数。我们考虑这样的问题，如信息一世和j都是朋友ķ使它更有可能一世和j自己是朋友。除其他外，我们展示了对于固定集小号和吨, 朋友越多一世有在小号，然后随机更多的朋友一世有在吨. 我们考虑友谊悖论的变体如何应用于我们的模型。我们还研究了社区中没有朋友的个体数量的分布，并得出了它与具有相同均值的泊松之间的总变异距离的界限。