Re: [igraph] eigenvector cumulative distribution

[Diamantis Sellis]

>From my experience with power-laws not related to networks cumulative
plots are much more useful as:
1. they have less noise especially in the rare(large) values
2. they do not require any kind of binning (important for small samples)
3. I think they are more robust. I tried taking sub-samples of my power-law 
distributed sample
   and the cumulative plots where always more similar to the cumulative of the 
whole sample.
Two nice papers that talk mention the advantages of using cumulative plots when 
dealing with power-laws:
- arXiv:cond-mat/0412004v3 [cond-mat.stat-mech] "Another, and in many ways a 
superior, method of plotting the data is to calculate a cumulative distribution 
function."
 - arXiv:0706.1062v2 [physics.data-an]


----- Original Message -----
From: "simone gabbriellini" <address@hidden>
To: "Help for igraph users" <address@hidden>
Sent: Wednesday, March 18, 2009 9:26:47 AM GMT -08:00 US/Canada Pacific
Subject: Re: [igraph] eigenvector cumulative distribution

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
>
>
> _______________________________________________
> igraph-help mailing list
> address@hidden
> http://lists.nongnu.org/mailman/listinfo/igraph-help



_______________________________________________
igraph-help mailing list
address@hidden
http://lists.nongnu.org/mailman/listinfo/igraph-help