State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, Zhejiang, China.
State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, Zhejiang, China;
Proc Natl Acad Sci U S A. 2019 Jul 30;116(31):15407-15413. doi: 10.1073/pnas.1801378116. Epub 2019 Jul 17.
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.
中心性被广泛认为是深入了解复杂网络结构和功能的最重要的度量之一。虽然已经提出了各种用于单层网络的中心性度量方法，但在多层网络（即多重中心性）中研究中心性的通用框架仍然缺乏。在这项研究中，引入了一种基于张量的框架来研究特征向量多重中心性，这使得可以量化层间影响对多重中心性的影响，提供了一种系统的方法来描述多重中心性如何在不同层之间传播。该框架可以利用关于层间相互作用的先验知识，以便更好地描述不同情况下的多重中心性。通过选择适当的层间影响函数和设计算法来计算特征向量多重中心性，提出了两个有趣的案例来说明如何对多层影响进行建模。该框架被应用于分析几个经验性的多层网络，结果证实它可以有效地量化层间的影响和节点的多重中心性。
