Multi-species grandcanonical models for networks with reciprocity
Abstract
Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates networks with this nontrivial property. Here we propose a grandcanonical class of models reproducing the observed patterns of reciprocity by regarding single and double links as Fermi particles of different `chemical species' governed by the corresponding chemical potentials. Within this framework we find interesting special cases such as the extensions of random graphs, the configuration model and hidden-variable models. Our theoretical predictions are also in excellent agreement with the empirical results for networks with well studied reciprocity.
Cite
@article{arxiv.cond-mat/0506494,
title = {Multi-species grandcanonical models for networks with reciprocity},
author = {Diego Garlaschelli and Maria I. Loffredo},
journal= {arXiv preprint arXiv:cond-mat/0506494},
year = {2007}
}
Comments
4 pages, 1 figure