Critical behavior and robustness evolution of (k,d)-core percolation in higher-order asymmetric dependency networks

Real-world networks frequently exhibit both higher-order multi-body interactions and asymmetric dependencies, while the traditional symmetric models based on pairwise links fail to accurately capture the cascading failure mechanisms inherent in such networks. For this study, we generalize the k -core percolation framework to higher-order topological structures by constructing an asymmetric dependency network model based on d -simplices, and formalize the ( k , d ) -core structure. By deriving higher-order self-consistent equations, the theoretical analysis reveals that the strict downward-closed geometric constraints of simplices significantly amplify the propagation of local failures, ruling out continuous phase transitions under the asymmetric dependency rule and simplicial construction adopted in this study. Specifically, when the coreness k ≥ 2 and dimension d ≥ 2 , the entire network inevitably undergoes a sudden, discontinuous phase transition (avalanche effect) under external perturbations. Furthermore, a “cross-layer firewall” effect exhibited by higher-order hub nodes under asymmetric protection is observed, which implies that the significant high-order degree differences can effectively block cross-layer cascading failures. Targeting at the strong robustness of hub nodes in high-order networks but the fragility of edge simplices, one novel simplicial dimensionality reduction attack (SDR-Attack) strategy is put forward. The given strategy can avoid the protected hub nodes and accurately strike the high-order simplex coronal clusters in critical states. Simulation results demonstrate that SDR-Attack possesses substantially greater destructive power than traditional hub-based attacks at an extremely low cost. This study provides new theoretical insights into the vulnerability assessment and structural optimization of higher-order complex networks.