Robustness of higher-order networks with synergistic protection

From chemical reactions to human communications, higher-order interactions are ubiquitous in real-world networks. Entities within higher-order interactions often exhibit collective behaviors that could create synergistic effects on robustness of the underlying system. Here we propose an analytical model to investigate the robustness of higher-order networks, in which potential higher-order synergistic protection is incorporated. In this model, higher-order networks are described with simplicial complexes, and robustness is studied under the proposed dynamics of extended bond percolation. We provide theoretical analysis for robustness quantities including the relative size of the giant component and percolation threshold. We discover that the percolation threshold could drop to zero, which is an indicator of notably strong robustness, with synergistic protective effects and dense higher-order simplices. We also find that higher-order interactions have strong impacts on the association between robustness and clustering. Specifically, a larger clustering coefficient could invariably indicate stronger robustness once the strength of protective effects exceeds a certain value. Our theoretical solutions are verified by simulation results in simplicial complexes with Poisson, exponential and power-law distributions.