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Re: [igraph] cohesive.blocks()

From: Gabor Csardi
Subject: Re: [igraph] cohesive.blocks()
Date: Wed, 30 Apr 2008 13:32:47 +0200
User-agent: Mutt/1.5.13 (2006-08-11)

On Wed, Apr 30, 2008 at 06:54:28PM +0900, MATSUDA, Noriyuki wrote:
> Hello:
>    I know cohesive.blocks() extracts two blocks that are cliques.
>       block4:   {1-7}
>       block 5:  {7,8,11,14)

Block 4 is not a clique in your example. That subgraph has only 18 edges,
a full graph on 7 vertices has 21. You can also see this from 
gb$block.cohesion, for a 7-clique it would be 6, but it is 5.

> But, I have an impression, from the explanations about Figures 2
> and 3 in Moody and White's paper, another one is embedded in
> the figures:
>         {17,18,19,20,21,22,23}  (not a clique)

This subgraph has cohesion 2, just like block 2 in which it is 
included. That's why it is not shown as a cohesive block. 
Basically, any subset of block 2 has at least cohesion 2, 
by definition.

>    This is derivable from the output of cohesive.blocks().  


> Yet I'd
> be happy if the group were directly obtainable, if it is cohesive (
> to a lesser extent than a clique).

The concept of 'cohesive' is well defined, and according to 
this definition 17:23 is not more cohesive than block 2, in which
it is embedded. If you want to have all subsets of vertices 
that have at least cohesion 2, then generate all possible subsets 
of block 2 and 3. I can't really understand why you would want 
this, though.


>     I know that  a set {8, 9, 10, 11, 12, 14, 15} is not cohesive.
> Thanks.

Csardi Gabor <address@hidden>    UNIL DGM

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