A tensor-based framework for studying eigenvector multicentrality in multilayer networks

Significance It is of significant interest to understand the structure and function of multilayer networks, which model many practical complex systems. Centrality, quantifying the importance of nodes in a graph, is widely recognized as one of the most effective measures. Nevertheless, a general framework for characterizing centrality in multilayer networks is still lacking. In this article, we fill this gap by developing a tensor-based framework for characterizing eigenvector multicentrality in general multilayer networks. We prove the existence and uniqueness of eigenvector multicentrality for 2 interesting scenarios, using the proposed framework. The results from empirical networks demonstrate that this framework helps us obtain a clear understanding of the eigenvector multicentrality of nodes. Centrality is widely recognized as one of the most critical measures to provide insight into the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.

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