power_law - Sample N integers from a discrete power-law distribution
power_law gamma k_min k_max N
power_law samples N elements from the discrete power-law
distribution
P(k) ~ k^{gamma}
where
k_min <= k <= k_max, gamma < 1
The program can be used to generate a power-law degree distribution with an assigned value of the exponent <gamma.
gamma: Exponent of the power-law distribution.
k_min, k_max: Boundaries of the sampling interval.
N The number of samples to generate
power_law prints on the standard output the sampled values, one per
line, in the format:
s1
s2
s3
...
sN
The program returns the value 0 if the sum of the samples is even,
or returns 1 otherwise. The return value can be used to determine
whether the set of samples can correspond to a degree sequence (if the
sum of the sequence is odd, then the sequence cannot be a valid degree
sequence). See RETURN VALUES below.
To generate N=1000 independent samples from the power-law
distribution P(k) ~ k^(-3), where samples are in the interval
[3, 50], we can use:
$ power_law -3.0 3 50 1000
11
3
3
5
6
7
....
8
3
$
To save the samples in the file pl_-3.0_3_50_1000, we redirect STDOUT:
$ power_law -3.0 3 50 1000 > pl_-3.0_3_50_1000
The value returned by power_law can be used to test whether the sum
of the resulting set of samples is even or odd. Under Windows
PowerShell, you can check the last exit code by inspecting the
variable $lastExitCode right after executing power_law, as in:
> power_law -2.7 4 300 5000 > pl_-2.7_4_300_5000
> $lastExitCode
0
>
In this case, the exit code is 0, meaning that the resulting set of
samples has an even sum (and can be thus used as a degree
sequence). Under Linux/MacOS/Unix (and in general when using any
POSIX-compliant shell) you should check the value of the variable
$?, right after executing power_law, i.e.:
$ power_law -2.5 3 500 5000 > pl_-2.5_3_500_5000
$ echo $?
1
$
Notice that this particular run of power_law has produced a sequence
with an odd sum, which thus cannot correspond to a valid degree sequence.
deg_seq(1), conf_model_deg(1), conf_model_deg_nocheck(1)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 5, Cambridge University Press (2017)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 9, Cambridge University Press (2017)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.