Analyzing Communicability and Connectivity in the Indian Stock Market During Crises

ArXiv ID: 2502.08242 “View on arXiv”

Authors: Unknown

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.

Keywords: communicability, financial networks, systemic risk, permutation methods, machine learning classification, equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced network theory concepts like communicability and hyperbolic geometry, increasing mathematical complexity, while also conducting statistical tests, permutation methods, and using ML classification on real financial data, demonstrating high empirical rigor.

  flowchart TD
    A["Research Goal:<br>Analyze information flow in Indian<br>stock market during crises"] --> B["Data: NIFTY 50 stocks<br>Periods: GFC & COVID-19"]
    B --> C["Network Construction:<br>Correlation-based networks"]
    C --> D["Key Metric Computation:<br>Communicability vs Shortest Path"]
    D --> E["Statistical Analysis:<br>Permutation tests for significance"]
    E --> F["Machine Learning:<br>Classification model features"]
    F --> G["Key Findings:<br>70-80% of stock pairs show<br>significant communicability shifts<br>Communicability outperforms shortest<br>path in crisis detection<br>Geometric measures comparable to<br>topology-based measures"]