generating a community graph in igraph

Question

I have been searching for an answer to this question but could not find any mention, so I decided to post here. I am trying to see if igraph or any packages provide a simple way to create a "community graph" where each node represents a community in the network and the ties represent ties between the communities. I can get the community detection algorithm to work fine in igraph, but I could not find a way to collapse the results to just show connections between each community. Any assistance would be appreciated.

Answer 1

You can simply use the contract.vertices() function. This contracts groups of vertices into a single vertex, essentially the same way you want it. E.g.

library(igraph)

## create example graph
g1 <- graph.full(5)
V(g1)$name <- 1:5    
g2 <- graph.full(5)
V(g2)$name <- 6:10
g3 <- graph.ring(5)
V(g3)$name <- 11:15
g <- g1 %du% g2 %du% g3 + edge('1', '6') + edge('1', '11')

## Community structure
fc <- fastgreedy.community(g)

## Create community graph, edge weights are the number of edges
cg <- contract.vertices(g, membership(fc))
E(cg)$weight <- 1
cg2 <- simplify(cg, remove.loops=FALSE)

## Plot the community graph
plot(cg2, edge.label=E(cg2)$weight, margin=.5, layout=layout.circle)