Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade

TL;DR

This paper introduces a stochastic link reversal symmetry to better understand reciprocity in directed networks, applying it to the international trade network to reveal how economic space influences network evolution and symmetry breaking.

Contribution

It develops a stochastic formalism for link reversal symmetry and applies it to analyze reciprocity and symmetry breaking in the world trade network.

Findings

Economic space embedding influences network symmetries.

Reciprocity evolution aligns with symmetry breaking in production space.

Stochastic symmetries help identify underlying mechanisms in networks.

Abstract

We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in economic space determines particular symmetries of the network, while the observed evolution of reciprocity is consistent with a symmetry breaking taking place in production space. Our results show that networks can be strongly affected by symmetry-breaking phenomena occurring in embedding spaces, and that stochastic network symmetries can successfully suggest, or rule out, possible underlying mechanisms.