Re: [igraph] How to find out whether a graph follows Guassian (normal) or power law distribution without looking at their shape?

[Horváth Árpád]

 shahab írta (Dátum: 2011. Mar. 04.)
> My question is if you have a graph file (in some format) How you can
> find out whether a graph follows Guassian (normal) or power law
> distribution without  looking at their shape and just by measuring
> some properties?
> or what is (in/out) degree distribution without looking at their
> shape? are there any metrics that someone can measure and say for
> example, is not power-law??
> 
> Any comment or reference is appreciated.

Dear shahab,

A reference:

@article{clauset-2007,
  url = { http://arxiv.org/abs/0706.1062 },
  author = {Aaron Clauset and Cosma Rohilla Shalizi and M.~E.~J. Newman},
  title = {Power-law distributions in empirical data},
  year = {2007},
  abstract = {{Power-law distributions occur in many situations of scientific
interest and have significant consequences for our understanding of natural and
man-made phenomena. Unfortunately, the detection and characterization of power
laws is complicated by the large fluctuations that occur in the tail of the
distribution -- the part of the distribution representing large but rare events
-- and by the difficulty of identifying the range over which power-law behavior
holds. Commonly used methods for analyzing power-law data, such as
least-squares fitting, can produce substantially inaccurate estimates of
parameters for power-law distributions, and even in cases where such methods
return accurate answers they are still unsatisfactory because they give no
indication of whether the data obey a power law at all. Here we present a
principled statistical framework for discerning and quantifying power-law
behavior in empirical data. Our approach combines maximum-likelihood fitting
methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic
and likelihood ratios. We evaluate the effectiveness of the approach with tests
on synthetic data and give critical comparisons to previous approaches. We also
apply the proposed methods to twenty-four real-world data sets from a range of
different disciplines, each of which has been conjectured to follow a power-law
distribution. In some cases we find these conjectures to be consistent with the
data while in others the power law is ruled out. }},
}

Tamas has a C code that do this evaluation.

Arpad


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