about power.law.fit

power.law.fit simply ML fits the 'prob(d) = d^\alpha' model to the
input, where d is positive integer. It seems to work for me:

data <- sample(1:10000, prob=(1:10000)^-3, rep=TRUE)
power.law.fit(data)

Call:
mle(minuslogl = mlogl, start = list(alpha = start))

Coefficients:
   alpha
3.017056

data <- sample(1:10000, prob=(1:10000)^-2, rep=TRUE)

Warning message:
In sample(1:10000, prob = (1:10000)^-2, rep = TRUE) :
  Walker's alias method used: results are different from R < 2.2.0

power.law.fit(data)

Call:
mle(minuslogl = mlogl, start = list(alpha = start))

Coefficients:
   alpha
2.016645

It returns with an "mle" object, so you can call 'confint',  'logLik',
etc. on it, see "mle-class" for details.

tmp <- power.law.fit(data)
summary(tmp)

Maximum likelihood estimation

Call:
mle(minuslogl = mlogl, start = list(alpha = start))

Coefficients:
      Estimate Std. Error
alpha 2.016645 0.01085921

-2 log L: 32150.62

confint(tmp)

Profiling...
   2.5 %   97.5 %
1.995522 2.038091

Gabor

ps. there is also an igraph-help mailing list, FYI. Just in case I
miss your questions here....

Dear all,

I'm using igraph for some analysis about the network I have. I have a
question about the function "power.law.fit".

I wonder if there is any test for checking whether the  "power.law.fit" is
good for the input, i.e., under which situation, could we use this function
to get a reliable result. I'm afraid even I input a random graph without any
property of "power-law" characteristics, it will returns an outcome which
seems to be a fit to available data while it has no meaning to us. Is there
any index like "goodness of fit" ?

Thank you for any comments.

Best!
Weijia

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Gabor Csardi <Gabor.Csardi at unil.ch>     UNIL DGM