2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121165Reciprocity 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.4 pages, 1 figureDisordered Systems and Neural NetworksStatistical MechanicsAdaptation and Self-Organizing SystemsData Analysis, Statistics and Probabilitytext