Fitness centrality: a non-linear centrality measure for complex networks

As often happens in science, tools, and methods originally developed in one field can unexpectedly become useful in others. This paper explores the formalism of Economic Fitness Complexity (EFC), initially designed to predict and explain the economic trajectories of countries, cities, and regions, which has also proven applicable in diverse contexts such as ecology and chess openings. The success of EFC is attributed to its ability to indirectly assess hidden capabilities within a system. However, existing EFC algorithms are constrained to bipartite graphs, becoming inapplicable even with minor deviations in the bipartite structure. This paper introduces an extension of EFC and its cousin Economic Complexity Index that applies to any graph, thereby overcoming the bipartite constraint. This extension introduces fitness centrality, a novel centrality measure that can be used for assessing node vulnerability. By broadening the scope of economic complexity analysis to diverse network structures, this work expands the applicability and robustness of EFC in complexity science.