We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied.
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A. Tacchella, M. Cristelli, G. Caldarelli, A. Gabrielli, L. Pietronero, Sci. Rep. 2, 723 (2012)
R.C. Feenstra, R.E. Lipsey, H. Deng, A.C. Ma, H. Mo, World trade flows: 1962–2000. Technical report (National Bureau of Economic Research, 2005)
G. Gaulier, S. Zignago, Baci: International trade database at the product-level. Centre d’Etudes Prospectives et d’Informations Internationales (2010), http://www.cepii.fr/anglaisgraph/workpap/pdf/2010/wp2010-23.pdf
B. Balassa, Manchester School 33, 99 (1965)
M. Cristelli, A. Gabrielli, A. Tacchella, G. Caldarelli, L. Pietronero, PLoS ONE 8, e70726 (2013)
R.J. Barro, X. Sala-i Martin, Economic Growth (MIT Press, 2004)
G. Caldarelli, Scale-free Networks: Complex Cebs in Nature and Technology (Oxford University Press, 2004)
S. Brin, L. Page, in Computer Networks and ISDN Systems (1998), p. 107
C. Hidalgo, R. Hausmann, Proc. Natl. Acad. Sci. USA, 106, 10570 (2009)
D. Ricardo, On the Principles of Political Economy and Taxation (John Murray, 1817)
A. Zaccaria, M. Cristelli, R. Kupers, A. Tacchella, L. Pietronero, J. Econom. Interact. Coord. 11, 151 (2016)
A. Zaccaria, M. Cristelli, A. Tacchella, L. Pietronero, PLoS ONE 9, e113770 (2014)
E. Pugliese, G.L. Chiarotti, A. Zaccaria, L. Pietronero, Complex economies have a lateral escape from the poverty trap [arXiv:1511.08622] (2015)
M. Cristelli, A. Tacchella, L. Pietronero. PLoS ONE 10, e0117174 (2015)
M. Cristelli, A. Tacchella, A. Zaccaria, L. Pietronero, Growth Scenarios for Sub-Saharan Countries in the Framework of Economic Complexity (2015) https://mpra.ub.uni-muenchen.de/71594/
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Pugliese, E., Zaccaria, A. & Pietronero, L. On the convergence of the Fitness-Complexity algorithm. Eur. Phys. J. Spec. Top. 225, 1893–1911 (2016). https://doi.org/10.1140/epjst/e2015-50118-1