How to find measures after community detection in igraph (R)?

Question

I am working with Community Detection in graphs. I have been through the different community detection algorithms implemented in igraph and plotting the community structures. Now after getting the communities object for different algorithms, I want to compare the algorithms based on different measures like density,cut ratio, coverage. (I know that modularity is already implemented). I can obtain a subgraph and then calculate the intra-cluster density but to find the inter-cluster density, I dont not know how to proceed. This is the code I have been using to find intra-cluster density:

karate <- graph.famous("Zachary")
wckarate <- walktrap.community(karate) #any algorithm
subg1<-induced.subgraph(karate, which(membership(wckarate)==1)) #membership id differs for each cluster
intradensity1 <- ecount(subg1)/ecount(karate) #for each cluster

Similarly I could proceed for each cluster and add all the densities or take the average of the all. My question is that if the number of communities is very large, then how to proceed?

And if I want to extract the number of edges between different communities, is there a nice way to extract the number of edges?

Please pardon me if this question is already asked. I am novice to igraph and R.

Answer 1

Well, we can just adapt your code to loop over the different subgroups

karate <- graph.famous("Zachary")
wckarate <- walktrap.community(karate) #any algorithm
sapply(unique(membership(wckarate)), function(g) {
    subg1<-induced.subgraph(karate, which(membership(wckarate)==g)) #membership id differs for each cluster
    ecount(subg1)/ecount(karate)
})

and as far as getting the edges between the communities, you could do

#get all combinations of communities
cs <- data.frame(combn(unique(membership(wckarate)),2))
cx <- sapply(cs, function(x) {
    es<-E(karate)[V(karate)[membership(wckarate)==x[1]] %--% 
              V(karate)[membership(wckarate)==x[2]]]    
    length(es)
})
cbind(t(cs),cx)

Also you can plot the communities to make sure that looks reasonable

plot.communities(wckarate, karate)