When Robust Isn’t Resilient: Quantifying Budget-Driven Trade-Offs in Connectivity Cascades with Concurrent Self-Healing

Cascading link failures continue to imperil power grids, transport networks, and cyber-physical systems, yet the relationship between a network’s robustness at the moment of attack and its subsequent resiliency remains poorly understood. We introduce a dynamic framework in which connectivity-based cascades and distributed self-healing act concurrently within each time-step. Failure is triggered when a node’s active-neighbor ratio falls below a threshold φ; healing activates once the global fraction of inactive nodes exceeds trigger T and is limited by budget B. Two real data sets—a 332-node U.S. airport graph and a 1133-node university e-mail graph—serve as testbeds. For each graph we sweep the parameter quartet (φ, B, T,attackmode) and record (i) immediate robustness R, (ii) 90% recovery time T90, and (iii) cumulative average damage. Results show that targeted hub removal is up to three times more damaging than random failure, but that prompt healing with B≥0.12 can halve T90. Scatter-plot analysis reveals a non-monotonic correlation: high-R states recover quickly only when B and T are favorable, whereas low-R states can rebound rapidly under ample budgets. A multiplicative fit T90∝B−βg(T)h(R) (with β≈1) captures these interactions. The findings demonstrate that structural hardening alone cannot guarantee fast recovery; resource-aware, early-triggered self-healing is the decisive factor. The proposed model and data-driven insights provide a quantitative basis for designing infrastructure that is both robust to failure and resilient in restoration.