The European Physical Journal Special Topics

, Volume 225, Issue 10, pp 1893–1911 | Cite as

On the convergence of the Fitness-Complexity algorithm

  • Emanuele Pugliese
  • Andrea ZaccariaEmail author
  • Luciano Pietronero
Regular Article Algorithm
Part of the following topical collections:
  1. Complex, Inter-networked Economic and Social Systems


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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Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  • Emanuele Pugliese
    • 1
    • 2
  • Andrea Zaccaria
    • 1
    • 2
    Email author
  • Luciano Pietronero
    • 2
    • 1
  1. 1.Istituto dei Sistemi Complessi, via dei Taurini 19RomaItaly
  2. 2.Sapienza Università di Roma, Piazzale Aldo Moro 2RomaItaly

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