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## [igraph] question on scale free networks

 From: Vincent Matossian Subject: [igraph] question on scale free networks Date: Sun, 4 Feb 2007 01:42:15 -0500

Hi,

I am trying to get a graph that has power-law probability distribution P(k) := k^ (-alpha)

I realize that in ba.game the above alpha is not the same as the 'power' parameter which controls the preferential attachment (I noticed that a power of 1 gives an alpha of ~2). Am I missing a mechanism that would give me a graph that has a final degree distribution as above by controlling alpha, for example a logarithmic slope of - 2.5, -2.1 or -3 ?

Thanks,

Vincent

PS
For example:

plotsf=function(ba,offset=0.0){
d=seq(0,max(degree(ba)))
n=vcount(ba)*degree.distribution(ba)

ld=log(d+offset,base=10)
ln=log(n+offset,base=10)

plot(ld,ln)
lfit<-lm(ln~ld)
abline(coef=coef(lfit))
print(coef(lfit))
}

ba=ba.game(10000,power=1)
plotsf(ba,-.5) # -.5 for adjustment for Inf values in computing log
# this returns a slope of -2
ba2=ba.game(10000,power=2)
plotsf(ba2,-.5)
# returns a slope of -0.6 but what control know would  get me a slope of -2.5 or  -3, ...?