Measuring node centrality when local and global measures overlap

Centrality metrics aim to identify the most relevant nodes in a network. In the literature, a broad set of metrics exists, measuring either local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the usual global centrality measures typically do not add significant information with respect to the degree, i.e., the simplest local metric. To extract different information from this class of networks, we propose the use of the Generalized Economic Complexity index (GENEPY). Despite its original definition within the economic field, the GENEPY can be easily applied and interpreted on a wide range of networks, characterized by high spectral gap, including monopartite and bipartite network systems. Tests on synthetic and real-world networks show that the GENEPY can shed light about the node centrality, carrying information generally poorly correlated with the node number of direct connections (node degree).