Re: [igraph] Eigenvector centrality

[Tamas Nepusz]

Hi Matthew,

> I am trying to understand eigenvector centrality, but I'm clearly  
> doing something wrong!
No, it seems you are doing everything right and the problem is within  
the eigenvector centrality calculation. The calculation calls ARPACK  
behind the scenes to do the hard job, and for some cases (like yours  
-- in fact, this is the only one we are aware of) it converges to the  
_second_ largest eigenvalue, not the first one. I tweaked the code  
yesterday a little bit, and it looks like if I set a random starting  
vector for ARPACK instead of the present solution (which uses the  
degree vector as the starting vector), the problem is solved. If you  
are willing to mess around with the igraph source code, this is the  
single line you have to change in igraph_eigenvector_undirected in  
centrality.c:

options->start=0;     /* random start vector */

Originally it was:

options->start=1;     /* no random start vector */

I will investigate the issue more in detail and try to come up with a  
permanent solution soon.

--
Tamas