Quantifying Propagation Risk in Distributed Critical Infrastructures: A Unified Framework for AI Failures and GPS Spoofing

Abstract We propose the Propagation Risk Index (PRI), a unified metric to quantify how erroneous information can spread across distributed infrastructures when failures are induced by AI systems or by exogenous GNSS/GPS spoofing. PRI integrates node-level error probability (p_i), resilience mechanisms (r_i), and criticality (c_i) with normalized connectivity (k_i), yielding an interpretable risk score with linear-time computation. We evaluate PRI in two settings: healthcare IT simulations and European-style aviation hub-and-spoke networks. Across scenarios, we observe hub-dominance patterns (≈ 62–90% contribution) and substantial risk reductions when resilience is targeted (≈ 46–65%). Comparisons with degree, betweenness, PageRank, and k-core indicate advantages for PRI when resilience and criticality are heterogeneous. We also provide an illustrative, correlational alignment with 2025 European GPS interference reports (e.g., Poland, Estonia; Lithuania via synthetic reconstruction) to contextualize orders of magnitude rather than establish causality. We include operational risk categories (Low < 0.002; Medium 0.002–0.004; High > 0.004), discuss limitations and assumptions, and outline extensions to temporal dynamics PRI(t). Code, data, and figure scripts are openly available on Zenodo to ensure full reproducibility.