NAME
tune_rho - Construct a multiplex with prescribed inter-layer correlations.
SYNOPSYS
tune_rho <rank1> <rank2> <rho> <eps> <beta> [RND|NAT|INV]
DESCRIPTION
This programs tunes the inter-layer degree correlation coefficient ρ (Spearman’s rank correlation) of two layers, by adjusting the inter-layer pairing of nodes. The files rank1 and rank2 are the rankings of nodes in the first and second layer, where the n-th line of the file contains the rank of the n-th node (the highest ranked node has rank equal to 1).
The parameter rho is the desired value of the Spearman’s rank correlation coefficient, while eps is the accuracy of rho. For instance, if rho is set equal to -0.25 and eps is equal to 0.0001, the program stops when the configuration of node pairing corresponds to a value of ρ which differs from -0.25 by less than 0.0001.
The parameter beta is the typical inverse temperature of simulated annealing.
If no other parameter is specified, or if the last parameter is RND, the program starts from a random pairing of nodes. If the last parameter is NAT then the program assumes that the initial pairing is the natural one, where the nodes have the same ID on both layers. Finally, if INV is specified, the initial pairing is the inverse pairing, i.e. the one where node 0 on layer 1 is paired with node N-1 on layer 2, and so on.
OUTPUT
The program prints on stdout a pairing, i.e. a list of lines in the format:
IDL1 IDL2
where IDL1 is the ID of the node on layer 1 and IDL2 is the corresponding ID of the same node on layer 2.
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