Re: [igraph] eigenvector cumulative distribution

[simone gabbriellini]

Gabor,

Following "On power-law relationships of the internet topology" by  
Faloutsos, Faloutsos and Faloutsos it looks like they never use  
cumulative frequencies, or they never use frequencies at all... they  
simply, for example, sort the nodes in decreasing order of outdegree  
(or eigenvector) and plot it against the rank of the node (its index  
in the order of decreasing outdegree).

However, in "Towards a Theory of Scale-Free Graphs: Definition,  
Properties, and Implications" by Lun Li, David Alderson , John C.  
Doyle, Walter Willinger it looks like cumulative size-rank  log-log  
plots are the more reliable tool for investigatin such type of  
relations.

but I have to admit I am walking on eggs... so I welcome every  
suggestion that can point me to understand if the evolution of my  
network has some scale-free properties.

best,
Simone



Il giorno 18/mar/09, alle ore 13:27, Gábor Csárdi ha scritto:

> Simone,
>
> On Wed, Mar 18, 2009 at 1:16 PM, simone gabbriellini
> <address@hidden> wrote:
> > Dear List,
> >
> > I see that it is always advisable to use cumulative log-log plot,  
> > like the
> > one on the igraph screenshot page
>
> I think this is not _always_ the case. If you have a power-law or
> exponential distribution, then the cumulative distribution is a
> power-law/exponential, too; and the cumulative distribution has less
> fluctuations usually.
>
> > (http://igraph.sourceforge.net/screenshots2.html#8), when  
> > investigating for
> > power law distributions...
> >
> > I was wondering how to build a cumulative distribution of  
> > eigenvalues.
> >
> > using for example:
> >
> > eigen<-evcent(g, scale=TRUE, weights = E(g)$weights)
> > eigenvector<-eigen$vector
> > dd<-as.numeric(table(eigenvector))
> > dd<-dd/sum(dd)
> >
> > I have a non cumulative distribution. How to make it cumulative?
>
> rev(cumsum(rev(dd)))
>
> Gabor
>
> > best regards,
> > Simone
> >
> >
> > _______________________________________________
> > igraph-help mailing list
> > address@hidden
> > http://lists.nongnu.org/mailman/listinfo/igraph-help
>
>
>
> --
> Gabor Csardi <address@hidden>     UNIL DGM
>
>
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