Spectral Hypergraph Algorithms for Early Detection of Connectivity Collapse with Application to Pharmaceutical Supply Chain Arrest

We propose a family of spectral hypergraph algorithms for early detection of connectivity collapse in pharmaceutical supply chain networks. The Fiedler eigenvalue λ2 of the normalised hypergraph Laplacian serves as the order parameter. Five geometry-aware early warning indicators (TSI, HSST, HOMFA, HOTV, ORC) monitor network topology rather than scalar residuals, with provable detection guarantees under geometric ergodicity. A Greedy Dejamming algorithm restores connectivity via rank-2 Laplacian updates, achieving a (1−1/e)-approximation within a procurement budget constraint. Monte Carlo validation on a calibrated pharmaceutical distribution hypergraph demonstrates substantially higher detection sensitivity and shorter lead times than classical statistical process control. Hyperedge representation yields detection gains exceeding 90% for simultaneous multi-party failures that pairwise graph projections miss entirely. A COVID-19 lockdown episode provides a held-out directional consistency check.