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Complex Networks and Symmetry I: A Review
Symmetry 2010, 2(3), 1710-1744; doi:10.3390/sym2031710

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

1,* , 2
1 Center for the Study of Complex Systems, University of Siena, Via Roma 56, 53100 Siena, Italy 2 LEM, Sant’Anna School of Advanced Studies, Piazza Martiri della Libertà 33, 56127 Pisa, Italy 3 Department of Chemistry, University of Siena, Via Aldo Moro 1, 53100 Siena, Italy
* Author to whom correspondence should be addressed.
Received: 25 August 2010 / Revised: 17 September 2010 / Accepted: 20 September 2010 / Published: 27 September 2010
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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.
Keywords: complexity; networks; symmetry breaking; World Trade Web complexity; networks; symmetry breaking; World Trade Web
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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