Clustering Coefficient

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已于 2022-08-10 20:21:34 修改 · 1.7k 阅读

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#聚类 #机器学习 #算法

于 2022-08-10 20:19:44 首次发布

本文介绍了网络分析中的聚类系数概念，包括聚类系数如何衡量网络中节点的聚类趋势，局部聚类系数和全局聚类系数的区别，并通过实例说明了如何计算这些指标。

Define

Clustering Coefficient：聚类系数

Clustering Coefficient measures the degree to which nodes in a network tend to cluster or form triangles.

——聚类系数衡量网络中节点倾向于聚类或形成三角形的程度

Triadic Closure

三元闭包

The tendency of people who share connections in a social network to become connected

“Triadic Closure would say that those edges that closed triangles are good candidate for edges that may show up next”

那些能形成闭合三角形的边，往往被认为是下一个会出现的边

但我们并不会总是有时间戳，也并不是总是知道边缘进入网路的顺序

Another way of referring to Triadic Closure is Clustering.

——另一种指代三元闭包的方式是聚类

Local Clustering Coefficient

局部聚类系数

We’re going to be measuring Clustering from the point of view of a single node.

——从单个顶点的角度测量聚类

define：

Fraction of pairs of the node’s friends that are friends with each other.
$\frac{\#\,\,\,of\,\,\,pairs\,\,\,of\,\,\,C's\,friends\,\,\,who \,\,\,are\,\,\,friends}{\#\,\,\,of \,\,\,pairs\,\,\,of\,\,\,C'\,friends}$
在这里插入图片描述

$instance\\ \#\,\,\,of\,\,\,C'\,friends=d_c=4(the\,\,\,degree\,\,\,of\,\,\,C)\\ \#\,\,\,of \,\,\,pairs\,\,\,of\,\,\,C'\,friends=\frac{d_c(d_c-1)}{2}=\frac{12}{2}=6\\ \#\,\,\,of\,\,\,pairs\,\,\,of\,\,\,C's\,friends\,\,\,who \,\,\,are\,\,\,friends=2\\ Local\,\,\,clustering\,\,\,coefficent\,\,\,of\,\,\,C=\frac{2}{6}=\frac{1}{3}$