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Re: [igraph] Question about fitting a line to a power-law distribution

From: Gábor Csárdi
Subject: Re: [igraph] Question about fitting a line to a power-law distribution
Date: Mon, 14 Feb 2011 10:57:23 +0100

On Mon, Feb 14, 2011 at 12:49 AM, Narges Zarabi <address@hidden> wrote:
> Dear all,
> I am trying to fit a straight line to the degree distribution of my network
> (which  is scale-free), using following commands:
> g <- barabasi.game(1000, directed =F)
> d <- degree(g)
> dd <- degree.distribution(g,cumulative=TRUE)
>  plot(dd,log="xy")
> alpha <- power.law.fit(d, xmin=10)
> lines(5:50, 10*(5:50)^(-coef(alpha)+1))
> but if I change the value xmin, the value of alpha changes and hence
> different straight line are generated! Is there a way to know which xmin is
> best to use? and which alpha and fitted line is more accurate?

Dear Narges,

I would fix an xmin value (say 20) and generate much larger networks,
e.g. with 1 million nodes, to have enough high degree vertices for the
fit. But I'm afraid there is no really principled way to determine
xmin, at least I don't know any. The larger your network is the less
it matters, AFAIK.


> Thanks in advance,
> Narsis
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> igraph-help mailing list
> address@hidden
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Gabor Csardi <address@hidden>     UNIL DGM

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