The Journal of China Universities of Posts and Telecommunications ›› 2023, Vol. 30 ›› Issue (6): 49-59.doi: 10.19682/j.cnki.1005-8885.2023.1016

Special Issue: 复杂网络传播与网络控制

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Node interdependent percolation of multiplex hypergraph with weak interdependence

Zhang Junjie, Liu Caixia, Liu Shuxin, Zang Weifei, Li Qian   

  1. 1. Institute of Information Technology, PLA Strategic Support Force Information Engineering University, Zhengzhou 450000, China
    2. Institute of System Engineering, Academy of Military Sciences, Beijing 100091, China
  • Received:2023-07-14 Revised:2023-10-02 Online:2023-12-28 Published:2023-12-28
  • Contact: Liu Shuxin
  • Supported by:
    This work was supported by the Major Science and Technology Program of Henan Province (221100210700 - 2).


In recent years, there has been considerable attention and research on the higher-order interactions that are prevalent in various real-world networks. Hypergraphs, especially in the study of complex systems, are proved effective in capturing these interactions. To better characterize the model in reality, this paper proposes a theoretical model of node interdependent percolation in multiplex hypergraphs, considering “ weak ” interdependence. The proposed model includes pairwise and higher-order interactions, where the removal of nodes triggers cascading failures. However, interdependent nodes connected to failed nodes experience partial loss of connections due to “ weak” interdependence, reflecting the self-sustaining capabilities of real-world systems. Percolation theory is applied to the analysis to investigate the properties of the percolation threshold and phase transition. Both analysis and simulation results show that as the strength of interdependence between nodes weakens, the network transitions from a discontinuous to a continuous phase, thereby increasing its robustness.

Key words: node interdependent, percolation theory, hypergraph