Multi-species grandcanonical models for networks with reciprocity

Details Multi-species grandcanonical models for networks with reciprocity Multi-species grandcanonical models for networks with reciprocity

2005-06-20

arxiv.org/abs/cond-mat/0506494v1

Physical Review E 73, 015101(R) (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure

Scientific paper

10.1103/PhysRevE.73.015101

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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