library(igraph)
g=graph.famous("Zachary")
c=edge.betweenness.community(g)
a=membership(c)
c$merges
b=community.to.membership(g,c$merges,steps=33)
[1] 1 1 2 1 3 3 3 1 4 5 3 1 1 1 4 4 3 1 4 1 4 1 4 4 2 2 4 2 2 4 4 2 4 4
[1] 9 4 0 0 0 0 5 0 3 2 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 7 0 0 8
I expect b is same with membership(c) because there are 33 steps. But why is b different from membership(c)?
This seems to be a bug in igraph because even the following does not work:
> library(igraph)
> g <- graph.full(3)
> c <- edge.betweenness.community(g)
> community.to.membership(g, c$merges, steps=1)$membership
This gives me a membership vector of 1 2 0, which is clearly wrong; the correct result should be 1 0 0 or 0 1 1. Actually, you can fix the bug by subtracting 1 from the merge matrix:
> g <- graph.famous("zachary")
> c <- edge.betweenness.community(g)
> membership(c)
[1] 1 1 2 1 3 3 3 1 4 5 3 1 1 1 4 4 3 1 4 1 4 1 4 4 2 2 4 2 2 4 4 2 4 4
> community.to.membership(g, c$merges-1, steps=29)$membership
[1] 0 0 2 0 3 3 3 0 1 4 3 0 0 0 1 1 3 0 1 0 1 0 1 1 2 2 1 2 2 1 1 2 1 1
These two membership vectors are essentially the same (with a bit of reindexing). Note that you only need 29 steps to reach the same membership vector because there are 34 vertices in the graph and you have 5 communities, so you need to perform 34-5=29 merges. Performing 33 steps would get you a single community only.
I will file a bug report for this in igraph's bug tracker.