Entropy-Based Indicators of Critical Transitions in Power-Law Networks Under Progressive Node Removal

Power-law networks tolerate extensive random failures yet can collapse abruptly under targeted attacks, often with little warning from connectivity measures alone. We ask whether an information-theoretic rate of structural change can provide early warning of impending connectivity collapse in such networks, and under what conditions any such signal transfers across generative ensembles. We track EWMA-smoothed successive Kullback–Leibler divergence between adjacent empirical degree distributions in Chung–Lu scale-free graphs with 2 < γ < 3 under both random and targeted node removal. Using fixed, pre-specified detection rules that do not reference connectivity, we find that the signal departs from an initial low-activity baseline well before GCC collapse under random failure, a pattern confirmed on an empirical CAIDA AS-level Internet topology. Under targeted removal, the signal exhibits immediate disruption rather than advance warning. A degree-matched configuration-model experiment reveals that the same rule fails due to ensemble-induced threshold inflation, a mechanistically interpretable limitation on transferability that motivates ensemble-aware deployment of structural monitoring rules.