Re: [igraph] Correlation between eigenvector (evcent) and vertex strength (graph.strength)

[Tamás Nepusz]

Your graph contains many components, and the whole eigenvector centrality 
concept is ill-defined in case of disconnected graphs because the eigenvector 
centralities of different components are independent of each other (so there 
exist an infinite number of possible solutions for the equations that govern 
the calculation of the eigenvector centrality, and igraph may converge to any 
of those).

igraph’s eigenvector solver seems to favour larger components; for instance, if 
you take the union of a ring graph of size 4 and a geometric random graph with 
100 vertices and a radius of 0.125, you will see that the vertices in the ring 
will almost always have zero eigenvector centrality, even though the average 
degree of both components is roughly the same.  

Anyway, if you really want to calculate eigenvector centrality for your 
network, you are strongly advised to do it for each component separately.  

--  
T.


On Tuesday, 17 December 2013 at 23:54, Hermann Norpois wrote:

> I hope the information transfer works. This is my code. The data
>  
> ch22.long.net (http://ch22.long.net)
> IGRAPH UNW- 76251 1899525 --  
> + attr: name (v/c), x (v/n), weight (e/n)
> evc <- evcent (ch22.long.net (http://ch22.long.net))
> ch22.long.deg <- graph.strength (ch22.long.net (http://ch22.long.net))
> plot (ch22.long.deg)
> plot (evc$vector)
>  
>  
> 2013/12/17 Hermann Norpois <address@hidden (mailto:address@hidden)>
> > Hello,
> >  
> > maybe I did not understand the concepts of graph.strenght and evcent but my 
> > guess was that the resultung vectors should be correlated in some way.
> > Using graph.strength (g) for an undirected weighted graph I get the 
> > strength of each vertex. The eigenvector of the adjacency matrix should 
> > reflect (somehow) the strengh of each vertex as well. But it doesnt (see 
> > attachment).
> >  
> > Can you please comment on this. Thanks
> > Hermann
> >  
> >  
> > My example:
> > evc <- evcent (g)
> > ev <- evc$vector
> >  
> > ch22.long.deg <- graph.strength (g)
> >  
> > and plotted the results (see attachment).
>  
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>  
>  
> Attachments:  
> - ev_deg.png
>