Characterizing the importance of nodes with information feedback in multilayer networks

Characterizing the importance of agents or events with possible related information is an important topic in information science. Due to the related agents and events usually can be described by the interconnected multilayer networks, so it is also one of the core themes in network-science. Previous researchers have proposed various tensor-based methods to discuss the centrality of interconnected multilayer networks, but the research on heterogeneous multilayer networks is insufficient. In this paper, based on PageRank algorithm in single-layer network, information feedback is introduced to describe the interaction among different layers. Then the coupled information feedback algorithm is developed to measure the centrality of the nodes in multilayer networks. First, the importance of nodes is measured according to PageRank in single network. Second, the links between the different layers are considered as the transmission and feedback paths for the information about the centrality of the nodes with interlayer links. This feedback mechanism could show us the global importance introduced by the interdependence of different layers. The feedback strength is parameterized and can be adjusted. With the feedback of information among different layers, an iterative update method for evaluating the importance of nodes in multilayer networks is constructed. Finally, several interesting cases are presented to illustrate how the feedback strength affects the rank of the nodes in the networks. The effectiveness of the proposed method is verified by an experimental analysis of the Author-Paper multilayer networks from the APS database and two other actual multilayer networks.