网络的平均聚类系数（igraph）

Question

我想计算图的平均聚类系数（来自 igraph 包）。但是，我不确定应该遵循哪种方法。

library(igraph)
graph <- erdos.renyi.game(10000, 10000, type = "gnm")

# Global clustering coefficient
transitivity(graph)
# Average clustering coefficient
transitivity(graph, type = "average")
# The same as above
mean(transitivity(graph, type = "local"), na.rm = TRUE)

我将不胜感激。

Answer 1

使用transitivity(graph)计算全局聚类系数（传递性）：

This is simply the ratio of the triangles and the connected triples in the graph. For directed graph the direction of the edges is ignored.

同时，transitivity(graph, type = "average")是transitivity(graph, type = "local")的平均值，首先计算局部聚类系数，然后取平均值：

The local transitivity of an undirected graph, this is calculated for each vertex given in the vids argument. The local transitivity of a vertex is the ratio of the triangles connected to the vertex and the triples centered on the vertex. For directed graph the direction of the edges is ignored.

参见，例如，?transitivity 和 Clustering coefficient。

所以首先它们都是有效的措施，选择应该取决于你的目的。它们之间的区别很明显（参见维基百科页面）：

It is worth noting that this metric places more weight on the low degree nodes, while the transitivity ratio places more weight on the high degree nodes. In fact, a weighted average where each local clustering score is weighted by k_i(k_i-1) is identical to the global clustering coefficient

其中 k_i 是顶点 i 邻居的数量。因此，也许同时使用它们也很公平。

Answer 2

transitivity(g, type="local")

输出向量的顺序如何？是否与以下顺序相同：

degree(g, mode="all")

度向量有索引但聚类系数没有

Answer 3

@Julius Vainora 回答了。对于那些试图为 type = "average" 做什么寻找答案的人的附加说明，因为 igraph 文档没有说明任何相关内容：

transitivity(graph, type = "average")

与

相同

transitivity(graph, type = "localaverage")

与

相同

transitivity(graph, type = "localaverageundirected")

与

相同

mean(transitivity(graph, type = "local"), na.rm = TRUE)

网络的平均聚类系数（igraph）

Average clustering coefficient of a network (igraph)

r

social-networking

igraph