Analyzing Communicability and Connectivity in the Indian Stock Market During Crises

TL;DR

This paper investigates how communicability, a network measure, captures information flow changes in the Indian stock market during crises, revealing significant shifts and improving market stability classification.

Contribution

It introduces the use of communicability metrics to analyze financial networks during crises, demonstrating their effectiveness over shortest-path measures in capturing systemic risk.

Findings

70-80% of stock pairs show significant communicability changes during crises.

Communicability measures outperform shortest-path metrics in classifying market states.

Geometric and topology-based measures have comparable performance.

Abstract

Understanding how information flows through the financial networks is important, especially during times of market turbulence. Unlike traditional assumptions where information travels along the shortest paths, real-world diffusion processes often follow multiple routes. To capture this complexity, we apply communicability, a network measure that quantifies the ease of information flow between nodes, even beyond the shortest path. In this study, we aim to examine how communicability responds to structural disruptions in financial networks during periods of high volatility. We compute communicability-based metrics on correlation-derived networks constructed from financial market data, and apply statistical testing through permutation methods to identify significant shifts in network structure. Our results show that approximately 70\% and 80\% of stock pairs exhibit statistically significant changes in communicability during the global financial crisis and the unprecedented COVID-19 crisis, respectively, at a significance level of 0.001. The observed shifts in shortest communicability path lengths offer directional cues about the nature and depth of each crisis. Furthermore, when used as features in machine learning classification models, communicability measures outperform the shortest-path-based measures in distinguishing between market stability and volatility periods. The performance of geometric measures was also comparable to that of topology-based measures. These findings offer valuable insights into the dynamic behavior of financial markets during times of crises and underscore the practical relevance of communicability in modeling systemic risk and information diffusion in complex networks.