The determination of the most central agents in complex networks is important because they are responsible for a faster propagation of information, epidemics, failures and congestion, among others. A challenging problem is to identify them in networked systems characterized by different types of interactions, forming interconnected multilayer networks. Here we describe a mathematical framework that allows us to calculate centrality in such networks and rank nodes accordingly, finding the ones that play the most central roles in the cohesion of the whole structure, bridging together different types of relations. These nodes are the most versatile in the multilayer network. We investigate empirical interconnected multilayer networks and show that the approaches based on aggregating—or neglecting—the multilayer structure lead to a wrong identification of the most versatile nodes, overestimating the importance of more marginal agents and demonstrating the power of versatility in predicting their role in diffusive and congestion processes.
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A.A., M.D.D., S.G. and A.S. were supported by the European Commission FET-Proactive project PLEXMATH (grant number 317614) and the Generalitat de Catalunya 2009-SGR-838. A.A. also acknowledges financial support from the ICREA Academia and the James S. McDonnell Foundation. S.G. and A.A. were supported by FIS2012-38266. E.O. is supported by DIM 2011–Région Île-de-France.
Supplementary Figures 1-6, Supplementary Tables 1-17, Supplementary Notes 1-7 and Supplementary References