Core-Periphery Dynamics in Market-Conditioned Financial Networks: A Conditional P-Threshold Mutual Information Approach

This study investigates how financial market structure reorganizes during the COVID-19 crash using a conditional p-threshold mutual information (MI) based Minimum Spanning Tree (MST) framework. We analyze nonlinear dependencies among the largest stocks from four diverse QUAD countries: the US, Japan, Australia, and India. Crashes are identified using the Hellinger distance and Hilbert spectrum; a crash occurs when HD = mu\_H + 2*sigma\_H, segmenting data into pre-crash, crash, and post-crash periods. Conditional p-threshold MI filters out common market effects and applies permutation-based significance testing. Resulting validated dependencies are used to construct MST networks for comparison across periods. Networks become more integrated during the crash, with shorter path lengths, higher centrality, and lower algebraic connectivity, indicating fragility. Core-periphery structure declines, with increased periphery vulnerability, and disassortative mixing facilitates shock transmission. Post-crash networks show only partial recovery. Aftershock analysis using the Gutenberg-Richter law indicates higher relative frequency of large volatility events following the crash. Results are consistent across all markets, highlighting the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability.