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Complex Networks and Symmetry I: A Review
Open AccessArticle

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

Center for the Study of Complex Systems, University of Siena, Via Roma 56, 53100 Siena, Italy
LEM, Sant’Anna School of Advanced Studies, Piazza Martiri della Libertà 33, 56127 Pisa, Italy
Department of Chemistry, University of Siena, Via Aldo Moro 1, 53100 Siena, Italy
Author to whom correspondence should be addressed.
Symmetry 2010, 2(3), 1710-1744;
Received: 25 August 2010 / Revised: 17 September 2010 / Accepted: 20 September 2010 / Published: 27 September 2010
PDF [727 KB, uploaded 27 September 2010]


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. View Full-Text
Keywords: complexity; networks; symmetry breaking; World Trade Web complexity; networks; symmetry breaking; World Trade Web

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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ruzzenenti, F.; Garlaschelli, D.; Basosi, R. Complex Networks and Symmetry II: Reciprocity and Evolution of World Trade. Symmetry 2010, 2, 1710-1744.

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