This paper develops a continuous functional framework for analyzing contagion dynamics in financial networks, extending the Navier-Stokes-based approach to network-structured spatial processes. We model financial distress propagation as a diffusion process on weighted networks, deriving a network diffusion equation from first principles that predicts contagion decay depends on the network's algebraic connectivity through the relation $\kappa = \sqrt{\lambda_2/D}$, where $\lambda_2$ is the second-smallest eigenvalue of the graph Laplacian and $D$ is the diffusion coefficient. Applying this framework to European banking data from the EBA stress tests (2018, 2021, 2023), we estimate interbank exposure networks using maximum entropy methods and track the evolution of systemic risk through the COVID-19 crisis. Our key finding is that network connectivity declined by 45\% from 2018 to 2023, implying a 26\% reduction in the contagion decay parameter. Difference-in-differences analysis reveals this structural change was driven by regulatory-induced deleveraging of systemically important banks, which experienced differential asset reductions of 17\% relative to smaller institutions. The networks exhibit lognormal rather than scale-free degree distributions, suggesting greater resilience than previously assumed in the literature. Extensive robustness checks across parametric and non-parametric estimation methods confirm declining systemic risk, with cross-method correlations exceeding 0.95. These findings demonstrate that post-COVID-19 regulatory reforms effectively reduced network interconnectedness and systemic vulnerability in the European banking system.

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