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

Abstract

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.