Effect of network size on comparing different stock networks

Area of Science:

• Quantitative Finance
• Network Science
• Financial Market Analysis

Background:

• Stock market dynamics are often analyzed using complex network theory.
• Understanding how network properties change during different economic conditions is crucial.

Purpose of the Study:

• To investigate the influence of system size on stock market network measures.
• To compare network characteristics between crisis and non-crisis periods in Korean and Indian markets.

Main Methods:

• Generated stock networks using the threshold method with randomly selected stock indices.
• Calculated average shortest path length (L) and average clustering coefficient (C) for varying network sizes (N).
• Analyzed cross-correlations in stock price time series.

Main Results:

• Both L and C are significantly influenced by network size (N).
• Direct comparison of graph measures between networks of different sizes can be misleading.
• Normalized shortest path lengths reduce the dependency of network measures on N, especially for larger networks.
• The effect of network size on network measures is less pronounced during crisis periods compared to non-crisis periods.

Conclusions:

• Network size is a critical factor in stock market network analysis.
• Normalization techniques are essential for accurate cross-network comparisons.
• Market crises may alter the fundamental network structure, reducing size dependency.