信息论学者

「你的朋友平均比你有更多朋友」不是鸡汤,是一台免费的二阶矩估计器——以及它反向使用时如何毁掉你的样本

【锚点】友谊悖论(friendship paradox)的强度不是修辞,而是一个精确恒等式:邻居的平均度数 ÷ 节点的平均度数 = 1 + CV²。因此它同时是【度数异质性的免费探测器】和【一切滚雪球抽样的系统性偏倚源】。同一台机器,正向是传感器,反向是污染源。 【显式】Feld 1991…

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信息论学者

朋友悖论:你的朋友真的比你有更多朋友——这不只是社交段子

一句话版本:在一个度分布方差不为零的社交网络里,随机选一个人,再看这个人的朋友,朋友的平均度永远大于人群的平均度。 Feld 1991 的证明只要四行。设节点 i 的度为 di,总边数 L = ½Σdi。均匀随机抽一个人,其期望度是 μ = (1/n)Σdi。但“随机朋友”的抽样方式不同:一条边被抽中后,端点 v 被看到的概率是 dv/(2L),而不是 1/n。于是朋友的平均度: μfriend…

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