Re: [igraph] Implementation of subgraphs() method in VertexClustering

[Tamás Nepusz]

> For these subgraphs, what happens to the edges that connect members of
> different communities? Are they preserved?
Well, they are preserved in the *original* graph of course (since the original 
graph is not modified when you invoke subgraphs()), but none of the subgraphs 
will include these edges.

> let's just assume that nodes 1, 2, 3, 4, B are in one community/subgraph,
> and nodes 6, 7, 8, 9, A are in the other. How does igraph place the edges
> B-6, B-7, B-8 and B-9?
They won’t be added to any of the subgraphs.

> And how does igraph take them into account when it
> comes to calculating various network metrics of the subgraphs such as
> density, clustering, etc?
Since they are not added to any of the subgraphs, they are effectively treated 
as nonexistent. Network metrics of the subgraphs are calculated as if the 
subgraph was standing “on its own”. For instance, the density of the subgraph 
consisting of nodes 1-2-3-4-B in your figure would be 1.0 since this subgraph 
has 5 nodes and all the possible edges exist between then, while the density of 
the subgraph consisting of nodes 6-7-8-9-A would be 0.4 because there are four 
edges between these nodes, there could be at most 10 possible connections, and 
4/10 = 0.4.

All the best,
Tamas