Order Structure Analysis of Node Importance by Super-adjacency Correlation Feature Temporal Evolution of Dynamic Multi-layer Network

Analyzing the order structure of node importance is not only one of the significant tasks in the field of social network research but also a proactive approach to comprehending the dynamics and structures of complex networks like communication, transportation, and medical networks. This research suggests a systematic modeling approach for capturing the temporal evolution of super-adjacency correlation in such networks in order to improve the description of complex systems in the actual world utilizing dynamic multi-layer networks. First, relying on the geometric projection relationship of the coupling between the multi-layer network layers, the tensor algebraic operation defines the correlation strength of nodes between layers in a dynamic multi-layer network at time t. Meanwhile, a super-adjacency matrix based on the approximate relationship between adjacent and cross-layer time layers of the dynamic multi-layer network at different times is constructed integrally. Second, the SIR model is used to confirm the model’s scientific validity. Node-important ranking in dynamic multi-layer networks is based on eigenvector centrality metrics. Finally, empirical data simulation indicates: The model in this study outperforms the aggregated temporal network in terms of Kendall’s τ values by an average of 15.2% and 13.29% across time layers, and the biggest Kendall’s τ values are 8.37% and 2.99% when compared to the SAM model. Thereby, the conclusions of those models demonstrate that the measurement of the super-adjacency correlation feature of a dynamic multi-layer network is scientific and effective.