如何计算R中的组间中心度

Question

I'm trying to implement a calculation of group centrality measures in a social network analysis.

Everett, MG, and SP Borgatti. “The Centrality of Groups and Classes.” The Journal of Mathematical Sociology 23, no. 3 (January 1999): 181–201. doi:10.1080/0022250X.1999.9990219.

I've managed to calculate the group closeness centrality, but I'm still having problems with the group betweenness centrality.

Having a igraph object net and a group, g , within this, I need to calculate two things 1) the number of shortest paths connecting every vertex that is NOT within the group (g), but which go through at least one of the vertices in group 2) the total number of shortest paths between all vertices not in the group.

Can anyone help me with some further code to do this.

I found something on the following link, but only a statement saying it should be possible: https://lists.nongnu.org/archive/html/igraph-help/2008-03/msg00043.html

UPDATE:::

I've now by trial and error managed to write following function to get all the shortest paths within a the non -group-part of a set of vertices that pass through another particular group in that set...

get.shortest.paths.throug.group<-function(graph, grp) {
num <- 1:vcount(graph)
y <- cbind(num, V(graph)$name)

no.group <- as.numeric(y[(y[,2] %in% grp)==FALSE, 1])
group <- as.numeric(y[(y[,2] %in% grp)==TRUE, 1])
group.chr <- as.character(y[(y[,2] %in% grp)==TRUE, 1])   
count <- vector(mode="numeric", length(group))    

paths <- lapply(1:(length(no.group)-1), function(i) {
get.all.shortest.paths(
  graph, 
  from = no.group[i],
  to = no.group[(i+1):length(no.group)]
)$res
})

list <- unsplit(paths, rep.int(seq_along(paths), sapply(paths, length)))

for (j in 1:length(group)) {
count[j] <-  sum(grepl(group.chr[j], list)*1)
}

gbc <- (2*sum(count)/length(list))/((vcount(graph)-length(group))*(vcount(graph)-length(group)-1))

return(gbc)
}

But... Since my network contains 7500 vetices; 118 in the group and 7382 non-group, this is a very time consuming function. Creating the list of all shortest.paths between the 7382 non-group vertices is not that time consuming, but the part of the function finding out which of the 31.000.000+ shortest.paths pass throug the group is very slow

for (j in 1:length(group)) { count[j] <- sum(grepl(group.chr[j], list)*1) }

Can this be done in a more effective way?

Someone wrote a java code http://sourceforge.net/p/jung/patches/12/ that does the calculations (apparently in a faster way). But I have no experience with java. Would it be possible to adapt the jung-patch to a R script??

Answer 1

Puzis et al give non-language-specific semicode for a fast scaleable algorithm here: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.76.056709

And a Python implementation here: http://ftp.aip.org/epaps/phys_rev_e/E-PLEEE8-76-064711/

My R is not good enough to implement it directly right now so unfortunately I don't have a final answer, but as a new user I also can't leave this in a comment. Good luck! And post if you do manage to implement it in R.