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From: | Tamas Nepusz |
Subject: | Re: [igraph] why different result for the same data set |
Date: | Fri, 23 Jan 2009 10:35:50 +0000 |
I tried the power.law.fit in igraph first, and get the alpha = 1.85. [...] However, when I use the plfit (http://www.santafe.edu/~aaronc/powerlaws/plfit.r ) to calculate the alpha again, I gotWell, fitting a power-law distribution to empirical data is a really tricky problem (see http://arxiv.org/abs/0706.1062) and the result you get depends heavily on the method you use and the cutoff point. The method of Clauset et al determines the cutoff point automatically based on a Kolmogorov-Smirnov test (iirc), while igraph simply takes the lowest value as the cutoff point unless you specify otherwise and then it simply uses a maximum likelihood estimation. You can see that the method of Clauset et al determined the most appropriate cutoff point as xmin=19; maybe you can try and re-run power.law.fit using xmin=19 and see whether the results differ.$xmin [1] 19 $alpha [1] 2.19 $D [1] 0.02631497.
-- Tamas
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