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) network framework. We analyze nonlinear dependencies among the largest stocks from four economically diverse QUAD countries: the United States, Japan, Australia, and India. The crash period is identified using the Hellinger distance and further characterized by the Hilbert spectrum. A crash is defined when the Hellinger distance exceeds the threshold, enabling the segmentation of the data into pre-crash, crash, and post-crash periods. To isolate direct stock-level dependencies, the conditional p-threshold MI approach filters out common market effects and applies permutation-based significance testing. The resulting statistically validated dependencies are used to construct MST networks, allowing consistent comparison across market periods. The network analysis reveals common crisis-related dynamics across all markets. During the crash, networks become more integrated, with shorter path lengths and higher centrality, while algebraic connectivity declines, indicating increased structural fragility. A clear reorganization of the core–periphery structure is observed, with declining core concentration and increasing periphery fragility, supported by disassortative mixing that facilitates shock transmission. In the post-crash period, network topology shows partial and non-uniform recovery, suggesting persistent structural effects. This interpretation is further supported by an aftershock analysis based on the Gutenberg–Richter law, which indicates a higher relative frequency of large volatility events following the crash. The consistency of these findings across all four markets highlights the effectiveness of the conditional p-threshold MI framework for capturing nonlinear interdependencies and systemic vulnerability in financial markets.