Quantifying the importance of specific types of higher-order structures in complex networks

Abstract

Identifying influential structures in complex networks is one of the most important and challenging problems to help optimize the network structure, control the spread of epidemics and accelerate information diffusion, etc. The structures in complex networks that can have the greatest impact on their structure and function are called the most important structures. In recent years, the identification of critical nodes (minimal structures) or edges in complex networks at the micro level has been widely studied and theories are maturing. At the macro level, the research on the effect of higher-order structure on network structure and function has been gradually enriched. However, there is relatively little research on how to quantify a specific type of higher-order structure in complex networks. In fact, sometimes the importance of individual nodes or edges in some real-world networks may not vary much but higher-order structures composed of different types of interconnected nodes or edges can have an important impact on the structure and function of the network. The research in this paper will enrich the development of this field. This paper proposes a new metric for evaluating significant structures in networks. It combines the local and semi-local topological properties of nodes and edges on the higher-order structure while considering the influence of the higher-order structure as a whole on the network structure and function, and its time complexity is close to linear which can be applied to large-scale networks. To verify the superiority of the proposed metric, the SI complex propagation model, network connectivity metric and structural richness are used. The simulation results show that the metric can more effectively and accurately identify the higher-order structures that have a significant impact on the network structure and function, compared with the four higher-order structure importance metrics we propose in 2 synthetic networks and 3 real networks. In addition, this paper also innovatively proposes an optimal parameter estimation method for nonlinear disturbance parameter g(t), which affects the propagation rate of complex propagated SI models.