Network Geometry of Borsa Istanbul: Analyzing Sectoral Dynamics with Forman-Ricci Curvature

This study investigates the dynamic interdependencies among key sectors of Borsa Istanbul-industrial, services, technology, banking, and electricity-using a novel network-geometric framework. Daily closure prices from 2022 to 2024 are transformed into logarithmic returns and analyzed via a sliding window approach. In each window, mutual information is computed to construct weighted networks that are filtered using Triangulated Maximally Filtered Graphs (TMFG) to isolate the most significant links. Forman-Ricci curvature is then calculated at the node level, and entropy measures over k-neighborhoods (k=1,2,3) capture the complexity of both local and global network structures. Cross-correlation, Granger causality, and transfer entropy analyses reveal that sector responses to macroeconomic shocks-such as inflation surges, interest rate hikes, and currency depreciation-vary considerably. The services sector emerges as a critical intermediary, transmitting shocks between the banking and both the industrial and technology sectors, while the electricity sector displays robust, stable interconnections. These findings demonstrate that curvature-based metrics capture nuanced network characteristics beyond traditional measures. Future work could incorporate high-frequency data to capture finer interactions and empirically compare curvature metrics with conventional indicators.