NODE AND LAYER. EIGENVECTOR CENTRALITIES FOR MULTIPLEX NETWORKS

摘要

Eigenvector-based centrality measures are among the most popular centrality measures in network science. The underlying idea is intuitive and the mathematical description is extremely simple in the framework of standard, mono-layer networks. Moreover, several efficient computational tools are available for their computation. Moving up in dimensionality, several efforts have been made in the past to describe an eigenvector-based centrality measure that generalizes the Bonacich index to the case of multiplex networks. In this work, we propose a new definition of eigenvector c engtrality that relies on the Perron eigenvector of a multi-humogeneous map defined in terms of the tensor describing the network. We prove that exestence and uniqueness of such centrality are guaranteed under very mild assumptions on the multiplex network. Extensive numerical studies are proposed to test the newly introduced centrality measure and to compare it to other existing eigenvector-based centralities.