On the convergence of the Fitness-Complexity algorithm

Abstract

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.

The complex dynamics of products and its asymptotic properties

“…This is because of a known phenomenon observed during the convergence of the map in Eq 6 defining Fitness and Complexity, namely that some values tend asymptotically to zero [34]. At the numerically estimated fixed point of the map, Complexity values span about 300 orders of magnitude, from 10 1 to 10 −300 , this number being limited only by computer precision.…”

Complex Economies Have a Lateral Escape from the Poverty Trap

“…We refer to [25] for a detailed description of the algorithm and a comparison with the one proposed by [17]. The convergence properties of the fitness and complexity algorithm are not trivial and have been studied in [26]. This methodology has been applied to both the study of specific geographical areas, such as the Netherlands ([27]) and the Sub-Saharan countries ([28]), and general features of growth and development ([9, 29]).…”

A Comparative Analysis of the Predictive Abilities of Economic Complexity Metrics Using International Trade Network

“…The procedure has been shown to perform well in an ecological network, by ranking the species according to their importance in the sustainability of the system [14]. The algorithm has been generalized by exponentiating the product term [15]. The iterative self-consistent set of equations is defined as…”