r - 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)

如果您能提供一些指导，我将不胜感激。

Answer 1

使用transitivity(graph)计算全局聚类系数(transitivity):

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并然后对它们进行平均:

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，?传递性和Clustering coefficient .

因此，首先这两种措施都是有效的，选择应该取决于您的目的。它们之间的区别非常明显(请参阅维基百科页面):

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是相当公平的。