Complex economic systems can often be described by a network, with nodes representing economic entities and edges their interdependencies, while network centrality is often a good indicator of importance. Recent publications have implemented a nonlinear iterative Fitness-Complexity (FC) algorithm to measure centrality in a bipartite trade network, which aims to represent the ‘Fitness’ of national economies as well as the ‘Complexity’ of the products being traded. In this paper, we discuss this methodological approach and conclude that further work is needed to identify stable and reliable measures of fitness and complexity. We provide theoretical and numerical evidence for the intrinsic instability in the nonlinear definition of the FC algorithm. We perform an in-depth evaluation of the algorithm’s rankings in two real world networks at the country level: the global trade network, and the patent network in different technological domains. In both networks, we find evidence of the instabilities predicted theoretically, and show that ‘complex’ products or patents tend often to be those that countries rarely produce, rather than those that are intrinsically more difficult to produce.

Counterintuitively, by joining the European Union, scientific collaboration in entrant countries became less international.