Rosario N. Mantegna investigates the hierarchical structure of stocks in financial markets using a topological approach. By analyzing the correlation coefficients between daily stock price differences, he constructs a graph representing the relationships between stocks. This graph is then used to determine a hierarchical tree, which reveals the underlying economic factors influencing stock price movements. The hierarchical tree is derived from a distance matrix based on the correlation coefficients, which is transformed into a metric that satisfies the properties of an Euclidean metric. This metric is used to construct a minimal spanning tree (MST), which provides a hierarchical organization of stocks. The MST is then used to identify groups of stocks that share common economic factors. The analysis is applied to two portfolios: one based on the Dow Jones Industrial Average and another on the Standard and Poor's 500 index. The results show that stocks within the same economic sector or subsector are grouped together in the hierarchical tree, indicating that they are influenced by similar economic factors. The study demonstrates that the hierarchical structure of stocks can be used to classify stocks based on their economic sectors and subsectors, providing valuable insights into the factors driving stock price movements. The findings support the idea that financial markets are complex systems influenced by multiple economic factors, and that the hierarchical structure of stocks can be used to understand these factors. The study also highlights the importance of using statistical methods to analyze financial data and uncover underlying economic patterns.Rosario N. Mantegna investigates the hierarchical structure of stocks in financial markets using a topological approach. By analyzing the correlation coefficients between daily stock price differences, he constructs a graph representing the relationships between stocks. This graph is then used to determine a hierarchical tree, which reveals the underlying economic factors influencing stock price movements. The hierarchical tree is derived from a distance matrix based on the correlation coefficients, which is transformed into a metric that satisfies the properties of an Euclidean metric. This metric is used to construct a minimal spanning tree (MST), which provides a hierarchical organization of stocks. The MST is then used to identify groups of stocks that share common economic factors. The analysis is applied to two portfolios: one based on the Dow Jones Industrial Average and another on the Standard and Poor's 500 index. The results show that stocks within the same economic sector or subsector are grouped together in the hierarchical tree, indicating that they are influenced by similar economic factors. The study demonstrates that the hierarchical structure of stocks can be used to classify stocks based on their economic sectors and subsectors, providing valuable insights into the factors driving stock price movements. The findings support the idea that financial markets are complex systems influenced by multiple economic factors, and that the hierarchical structure of stocks can be used to understand these factors. The study also highlights the importance of using statistical methods to analyze financial data and uncover underlying economic patterns.