Recovering Structural Organization in Noisy Correlation Networks Using Financial Systems as a Testbed

Empirical correlation matrices estimated from financial return time series are contaminated by statistical noise arising from finite sample size, obscuring genuine interactions among assets. We apply spectral decomposition to separate the empirical correlation matrix into a structured component associated with eigenvalues exceeding the Marchenko-Pastur bounds and a random component representing statistical noise. Using daily returns from the NIFTY 200, NIFTY 500, and S&P 500 over 2010-2022, we show that the structured component, constructed from only 10-16 eigenmodes, reproduces the main statistical properties of the full correlation matrix while removing most noise-dominated eigenmodes. Financial networks derived from the structured component exhibit significantly stronger and more stable core-periphery organization than networks constructed from the full or random matrices. Degree-preserving randomization, Kolmogorov-Smirnov, and Wasserstein distance tests confirm a clear statistical separation between structured and random components. We further show that structured networks display pronounced scale-free degree distributions in the Indian markets. As a practical application, portfolios constructed from peripheral assets of the denoised networks consistently outperform portfolios based on unfiltered correlations and standard benchmarks on a risk-adjusted basis, with robustness verified through Monte Carlo subsampling. These results demonstrate that spectral denoising effectively recovers meaningful network structure from noisy financial correlations.