igraph与tnet之间中心性度量的差异

Question

我正试图获得有针对性的加权网络的中心度量.我一直在使用igraph和tnet包R.但是,我发现使用这两个软件包获得的结果存在一些差异,我对这些差异的原因有点困惑.见下文.

require(igraph)
require(tnet)
set.seed(1234)

m <- expand.grid(from = 1:4, to = 1:4)
m <- m[m$from != m$to, ]
m$weight <- sample(1:7, 12, replace = T)
igraph_g <- graph.data.frame(m)
tnet_g <- as.tnet(m)

closeness(igraph_g, mode = "in")

         2          3          4          1 
0.05882353 0.12500000 0.07692308 0.09090909 

closeness(igraph_g, mode = "out")

         2          3          4          1 
0.12500000 0.06250000 0.06666667 0.10000000 

closeness(igraph_g, mode = "total")

         2          3          4          1 
0.12500000 0.14285714 0.07692308 0.16666667 


closeness_w(tnet_g, directed = T, alpha = 1)

     node closeness n.closeness
[1,]    1 0.2721088  0.09070295
[2,]    2 0.2448980  0.08163265
[3,]    3 0.4130809  0.13769363
[4,]    4 0.4081633  0.13605442

谁知道发生了什么事？

Answer 1

在发布这个问题之后,我偶然发现了一个由Tore Opsahl维护的博客,他是该tnet软件包的维护者.我使用博客的这篇文章中的评论问了同样的Tore问题.以下是Tore的回复:

感谢您使用tnet!igraph能够处理重量; 但是,距离函数igraph期望权重代表"成本"而不是"强度".换句话说,系带重量被认为是穿过系带所需的能量.请参阅加权网络中的最短路径.

因此,如果运行由Tore(需要的权重的逆传递它们到之前提供下面的代码igraph),则获得两个相等的紧密度得分tnet和igraph.

> # Load packages
> library(tnet)
>   
> # Create random network (you could also use the rg_w-function)
> m <- expand.grid(from = 1:4, to = 1:4)
> m <- m[m$from != m$to, ]
> m$weight <- sample(1:7, 12, replace = T)
>   
> # Make tnet object and calculate closeness
> closeness_w(m)

     node closeness n.closeness
[1,]    1 0.2193116  0.07310387
[2,]    2 0.3809524  0.12698413
[3,]    3 0.2825746  0.09419152
[4,]    4 0.3339518  0.11131725

>   
> # igraph
> # Invert weights (transform into costs from strengths)
> # Multiply weights by mean (just scaling, not really)
> m$weight <- mean(m$weight)/m$weight
> # Transform into igraph object
> igraph_g <- graph.data.frame(m)
> # Compute closeness
> closeness(igraph_g, mode = "out")

        2         3         4         1 
0.3809524 0.2825746 0.3339518 0.2193116