1. power_law(1)
2. www.complex-networks.net
3. power_law(1)

NAME

`power_law` - Sample N integers from a discrete power-law distribution

SYNOPSIS

`power_law` gamma k_min k_max N

DESCRIPTION

`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.

PARAMETERS

• gamma: Exponent of the power-law distribution.

• k_min, k_max: Boundaries of the sampling interval.

• N The number of samples to generate

OUTPUT

`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.

EXAMPLES

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
``````

RETURN VALUES

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.

REFERENCES

• 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)

AUTHORS

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.

1. www.complex-networks.net
2. September 2017
3. power_law(1)