AFAIK the network is not scale-free any more if the preferential attachment is not exactly linear. See, e.g.,: P.L. Krapivsky, S. Redner, and F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000).
T. Dear Tamas,
Thanks for your answer. Do you have any idea of how the value of alpha will change by changing the power argument? Is there a mathematical formula which defines the relationship?
Regards, Narsis On Sun, Feb 13, 2011 at 1:21 PM, Tamás Nepusz <address@hidden> wrote:
> I get an alpha = 2.8 , which is different from the power I used in building the graph. Does anyone have any explanation for this?
The power argument does not specify the alpha exponent of the degree distribution; it specifies the exponent used when igraph determines the attachment probabilities after a new vertex is added. power=1 corresponds to linear preferential attachment, which should indeed correspond to alpha = 3 in the infinite limit, so the value of 2.8 you get seems to be correct.
--
Tamas
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