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[igraph] igraph R: fit_power_law

From: Sander van Haperen
Subject: [igraph] igraph R: fit_power_law
Date: Mon, 5 Aug 2019 16:04:48 +0200

Dear reader, 

Many thanks for supporting the igraph package.
It continues to be indispensable for my research on digitally networked social movements.  

I have 3 questions about the function "fit_power_law". 
  1. The igraph documentation suggests that the bfgs function is used to estimate the power law alpha, but I think the C implementation relies on the  Broyden-Fletcher-Goldfarb-Shanno optimization function of the lbfgs library instead. Is that correct?
  2. The fit_power_law function relies on the MLE function of the stat4 package. I am curious why this was deprecated, given the availability of plfit and MLE parameters. Is this simply a memory issue? 
  3. How to interpret the p-value of the Kolmogorov-Smirnov test? The igraph help file states: "Small p-values (less than 0.05) indicate that the test rejected the hypothesis that the original data could have been drawn from the fitted power-law distribution" . The C implementation of the KS test in igraph uses the Hurwitz Zeta function. Shouldn't this mean that high p-values indicate a good model fit, as suggested by Clauset et al (2009:678)? 
Apologies if these questions are obtuse. I am not a trained programmer nor statistician, and could not solve these questions from any documentation or other source online. 

Thank you for your time and help.
Your work allows me to learn much about R (and networks!). 

Kind regards, 

Sander van Haperen
University of Amsterdam

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