Patterns of link reciprocity in directed networks

Details Patterns of link reciprocity in directed networks Patterns of link reciprocity in directed networks

2004-04-21

arxiv.org/abs/cond-mat/0404521v2

Phys. Rev. Lett. 93, 268701 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Final version accepted for publication on Physical Review Letters

Scientific paper

10.1103/PhysRevLett.93.268701

We address the problem of link reciprocity, the non-random presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.

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