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We explore the hypothesis that the relative abundance of feedback loops inmany empirical complex networks is severely reduced owing to the presence of aninherent global directionality. Aimed at quantifying this idea, we propose asimple probabilistic model in which a free parameter $\gamma$ controls thedegree of inherent directionality. Upon strengthening such directionality, themodel predicts a drastic reduction in the fraction of loops which are alsofeedback loops. To test this prediction, we extensively enumerated loops andfeedback loops in many empirical biological, ecological and socio-technological directed networks. We show that, in almost all cases, empiricalnetworks have a much smaller fraction of feedback loops than networkrandomizations. Quite remarkably, this empirical finding is quantitativelyreproduced, for all loop lengths, by our model by fitting its only parameter$\gamma$. Moreover, the fitted value of $\gamma$ correlates quite well withanother direct measurement of network directionality, performed by means of anovel algorithm. We conclude that the existence of an inherent networkdirectionality provides a parsimonious quantitative explanation for theobserved lack of feedback loops in empirical networks.

Inherent directionality explains the lack of feedback loops in empirical networks