Measuring nodes centrality when local and global measures overlap

Abstract

Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring 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 new 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 networks systems. Tests on synthetic and real-world networks show that the GENEPY can shed new light about the nodes centrality, carrying information generally poorly correlated with the nodes number of direct connections (nodes degree).