A General Framework of Studying Eigenvector Multicentrality in Multilayer Networks

Multilayer networks have drawn much attention in the community of network science recently. Tremendous effort has been invested to understand their structure and functions, among which centrality is one of the most effective approaches. While various metrics of centrality have been proposed for single-layer networks, a general framework of studying centrality in multiplayer networks is lacking. Here we introduce a mathematical framework to study eigenvector multicentrality, which enables us to quantify the relationship between interlayer influences and eigenvector multicentrality, providing an analytical tool to describe how eigenvector multicentralities of nodes propagate among different layers. Further, the framework is flexible for integrating prior knowledge of the interplay among layers so as to attain a tailored eigenvector multicentrality for varying scenarios. We show how to model the multilayer influences by choosing appropriate influence weight functions and design algorithms to calculate eigenvector multicentrality in various typical scenarios. We apply this framework to analyze several empirical multilayer networks, finding that it can quantify the influences among layers and describe the structure-function relationship of multilayer networks very well. ∗Correspondence: [email protected]. 1 ar X iv :1 70 8. 07 76 3v 1 [ ph ys ic s. so cph ] 2 5 A ug 2 01 7