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Multi-species grandcanonical models for networks with reciprocity

Diego Garlaschelli·Maria I. Loffredo
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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.

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Diego Garlaschelli, Maria I. Loffredo. 2005-06-20. Multi-species grandcanonical models for networks with reciprocity. https://doi.org/10.1103/physreve.73.015101

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