The Spectral Topology of Global Imbalances:A Graph-Theoretic Framework for Systemic Risk in the Balance of Payments
We model global balance-of-payments linkages as a directed weighted exposure network and study systemic fragility through the spectrum of the associated operators. From a signed bilateral-flow matrix, we construct a nonnegative exposure lift, derive a spectral stability criterion for linear propagation, and define node- and edge-level risk measures using Perron-Frobenius geometry, PageRank, and marginal spectral impact. We further give two complementary extensions: a directed Laplacian formulation for shock diffusion and a non-backtracking threshold for cascade formation on sparse exposure networks. The framework identifies systemic risk as a topological property of the global network rather than a collection of isolated country indicators, and it yields mathematically explicit diagnostics for resilience, concentration of stress, and targeted stabilization.