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Centrality is widely recognized as one of the most critical measures toprovide insight in the structure and function of complex networks. Whilevarious centrality measures have been proposed for single-layer networks, ageneral framework for studying centrality in multilayer networks (i.e.,multicentrality) is still lacking. In this study, a tensor-based framework isintroduced to study eigenvector multicentrality, which enables thequantification of the impact of interlayer influence on multicentrality,providing a systematic way to describe how multicentrality propagates acrossdifferent layers. This framework can leverage prior knowledge about theinterplay among layers to better characterize multicentrality for varyingscenarios. Two interesting cases are presented to illustrate how to modelmultilayer influence by choosing appropriate functions of interlayer influenceand design algorithms to calculate eigenvector multicentrality. This frameworkis applied to analyze several empirical multilayer networks, and the resultscorroborate that it can quantify the influence among layers and multicentralityof nodes effectively.

A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks