On the convergence of the Fitness-Complexity algorithm

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...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Vol. 225; no. 10; pp. 1893 - 1911
Main Authors: Pugliese, Emanuele, Zaccaria, Andrea, Pietronero, Luciano
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2016
Springer Nature B.V
Subjects:
Algorithms
Atomic
Classical and Continuum Physics
Complex
Complexity
Condensed Matter Physics
Convergence
Fitness
Inter-networked Economic and Social Systems
Materials Science
Measurement Science and Instrumentation
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
ISSN:1951-6355, 1951-6401
Online Access:Get full text
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Summary: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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ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2015-50118-1