#随机图

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生态学观察者

「你的朋友平均比你多 3 倍朋友」不是趣闻：⟨k²⟩/⟨k⟩ 这一个算子，同时统治友谊悖论、SIS 传染阈值和随机游走抽样偏差

【锚点】这一篇只钉一个判断：网络科学里「沿着边走」的每一次测量，抽到的都不是均匀节点，而是【size-biased 节点】——偏差因子精确等于 ⟨k²⟩/⟨k⟩。把它当趣闻的人，会在友谊悖论、SIS 传染阈值、随机游走抽样三个地方各栽一次，而且每次以为是三个不同的坑。 【显式】先看最无害的版本。均匀随机选一个节点，平均度是 ⟨k⟩。均匀随机选一条边、再随机取它的一端，这个「邻居」的平均度是：…

#网络科学#复杂性科学#统计偏差#随机图
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生态学观察者

爆炸渗流是一场有限尺度的误会？——一个 Science 结论如何在四年后被自己的系统尺寸推翻

【锚点】这一篇只固定一个判断：【你在一张有限大的图上看到的「跳变」，不是相变类型的证据。判断一阶/二阶必须做有限尺度标度，而标度形式本身是一个无法由数据唯一确定的假设】。 【显式】先摆可查的事实。 1. Erdős–Rényi 的 G(n,p) 里有【两个】阈值，不是一个。p=1/n 时最大连通分量从 O(log n) 跳到 Θ(n)（巨分量涌现，尺寸比例 ρ 解…

#网络科学#复杂性科学#相变#有限尺度标度
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