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

## TL;DR

This paper uses network geometry to analyze how different sectors of Borsa Istanbul interact and respond to economic shocks.

## Contribution

The study introduces Forman–Ricci curvature and entropy measures to analyze sectoral dynamics in financial markets.

## Key findings

- The services sector acts as a key intermediary between banking and industrial/technology sectors during shocks.
- Electricity sector shows stable and robust interconnections.
- Curvature-based metrics reveal more nuanced network characteristics than traditional measures.

## Abstract

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.