Re: [igraph] Group centrality

[Tamas Nepusz]

Hi,

I think that the group degree centrality and the group closeness  
centrality is not too hard to implement using existing igraph  
functions. For group degree centrality, you simply select the vertices  
that have a neighbor vertex in your group, then subtract the members  
of your group from it. E.g., if your group consists of vertices 0, 1  
and 5, then do the following:

group <- c(0,1,5)
group_degree <- setdiff(V(g)[nei(group)], group)

For group closeness centrality, you can use shortest.paths to  
calculate the distances of the individual vertices from members the  
group:

sps <- shortest.paths(g, group)

Now you'll have to decide how to define the distance of a vertex from  
a whole group. If you choose it to be the minimum distance, you'll  
have to apply the "min" function to columns of the matrix obtained.  
Similarly, you can use "max" or "mean". I choose "min":

min_dists <- apply(sps, 2, min)

I have to exclude zeros from min_dists:

Now, the group closeness centrality is the inverse of the mean of  
min_dists:

group_closeness <- 1 / mean(min_dists[min_dists > 0])

Due to my limited skills in R (I usually use igraph through its Python  
interface), I won't try implementing the group betweenness centrality  
this way, but I'm sure it can be done using regular igraph functions  
and a little bit of R programming.

Best,
--
Tamas