Network geometry, topology, and spectral analysis in global stock markets: Insights from using the Ricci curvature, Euler characteristic, and random matrix theory

The global stock market network exhibits complex patterns of interdependence that are central to systemic stability. This study proposes a multi-perspective framework integrating random matrix theory, Ricci curvature, and the Euler characteristic to characterize synchronization, geometric robustness, and global structural organization in financial networks. The maximum eigenvalue captures collective market behavior, Ricci curvature quantifies local fragility, and the Euler characteristic summarizes global topological cohesion.The framework is further complemented by entropy-based descriptors that capture spectral concentration and geometric heterogeneity, thereby provideng complementary multiscale descriptors to characterize of systemic fragility. Using daily data from major global stock indices (2017-2022), we identify pronounced structural transitions during the COVID-19 pandemic. The dynamic analysis also reveals a secondary structural reconfiguration in early 2022, temporally aligned with the Russia-Ukraine shock, suggesting that geometric and topological descriptors are sensitive to heterogeneous stress events. The results demonstrate that integrating spectral, geometric, and topological perspectives provides complementary insights into market resilience and crisis-driven structural change.