Re: [igraph] about ba.game

[Gábor Csárdi]

Hi,

On Tue, Jan 5, 2010 at 2:33 PM, gunce orman <address@hidden> wrote:
> Hello,
>
> I use ba.game funciton  to create a scale free network. And then I'm trying
> to calculate the exponent of power law for the different value of the
> parameter "power" of ba.game...  Is there any explication of the relation
> between that power parameter ( the alpha exponent of the choosing the
> vertices) and the gamma ( the exponent of the power low of the degrees) ???

the degree distribution is a power law only if the "power" parameter
is one. Otherwise it will be exponential. See e.g.
http://arxiv.org/abs/cond-mat/0005139

> If i'm not wrong, for power=1, normally gamma must be 3, because it is
> linear preferential attachement. But when I produce a set of network for
> power=1 and try to find their gamma values by using power.low.fit(), I have
> many different values than 3... Am I doing something wrong???

Tamás mentioned the finite size effect. Another thing is that ba.game
is a bit different from the model that was proven to lead to gamma=3,
e.g. ba.game does not generate loop edges. See
http://www3.interscience.wiley.com/journal/79502716/abstract

Gabor

> Thank you very much
>
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-- 
Gabor Csardi <address@hidden>     UNIL DGM