fit_knn

NAME

fit_knn - power-law fit of the inter-layer degree correlation function.

SYNOPSYS

fit_knn <filein> <alpha>

DESCRIPTION

Perform a power-law fit of the inter-layer degree correlation function:

where k is the degree of a node on layer 1, q is the degree on layer 2 and P(q|k) is the probability that a node with degree k on layer 1 has degree q on layer 2. The program assumes that q(k) can be written in the form ak^b, and computes the two parameters a and b through a linear fit of the log-log plot of q(k).

The input file filein contains a list of lines in the format:

  ki qi

where ki is the degree of node i at layer 1 and qi is the degree of node i at layer 2.

The second parameter alpha is the ratio of the progression used to generate the exponentially-distributed bins for the log-log plot. Typical values of alpha are between 1.1 and 2.0.

N.B.: The exponent b computed with this method is known to be inaccurate.

OUTPUT

The program prints on stdout the values of the parameters a and b of the power-law fit q(k) = ak^b.

REFERENCE

V. Nicosia, V. Latora, “Measuring and modeling correlations in multiplex networks”, Phys. Rev. E 92, 032805 (2015).

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.032805

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Growing multiplex networks”, Phys. Rev. Lett. 111, 058701 (2013).

Link to paper: http://prl.aps.org/abstract/PRL/v111/i5/e058701

V. Nicosia, G. Bianconi, V. Latora, M. Barthelemy, “Non-linear growth and condensation in multiplex networks”, Phys. Rev. E 90, 042807 (2014).

Link to paper: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.042807