Differences in centrality measures between igraph and tnet

Question

I'm trying to obtain centrality measures for a directed, weighted network. I've been using the igraph and tnet packages in R. However, I've discovered some differences in the results obtained using these two packages, and I'm a little confused about the cause of these differences. See below.

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

Anybody know what's going on?

Normalization, and also the order of the vertices might be different. I would draw a simple example and calculate closeness for that by hand, if you suspect one of them is wrong. — Gabor Csardi, Dec 05 '13 at 04:03
@Gabor Csardi thanks for your suggestions! I had already tried using the normalization option in the `closeness` function from `igraph` without success, and had also already noticed that the order of the closeness scores was a little weird from the `igraph` `closeness` function. As it turns out, the inconsistency was due to differences in how `igraph` and `tnet` treat the weights when calculating closeness. See my answer below for more details. — Patrick S. Forscher, Dec 05 '13 at 04:36

score 14 · Accepted Answer · edited Dec 05 '13 at 13:23

After posting this question, I stumbled upon a blog maintained by Tore Opsahl, maintainer of of the tnet package. I asked this same question of Tore using the comments on this post of the blog. Here is Tore's response:

Thank you for using tnet! igraph is able to handle weights; however, the distance function in igraph expects weights that represent 'costs' instead of 'strength'. In other words, the tie weight is considered the amount of energy needed to cross a tie. See Shortest Paths in Weighted Networks.

Thus, if you run the following code provided by Tore (which takes the inverse of the weights before passing them to igraph), you obtain equivalent closeness scores for both tnet and 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

Differences in centrality measures between igraph and tnet

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