High-Dimensional System Correlation Metrics Based on Higher-Order Information from Complex Networks

Big data has generated massive amounts of multi-source data and complex data correlations, making the efficient extraction of value from these correlations a major challenge in the field. The ongoing development of complex network theory has led to the widespread application of methods that mine system correlations based on network topology. However, if correlation analysis relies solely on low-order topological features, it will overlook higher-order connectivity information at the mesoscale. First, by leveraging complex network construction algorithms, we establish a multi-layer finite-transit visual graph network and develop metrics for measuring correlation and guidance relationships by integrating high-order network information. Second, simulation experiments were conducted on the CML system, the Lorenz system, and the Rössler system, respectively. By comparing the results with traditional low-order metrics and incorporating noise interference tests, the superiority, effectiveness, and robustness of the proposed metrics in identifying correlations were validated. Finally, empirical research was conducted using data from the China Carbon Emission Trade Exchange, the EU Emissions Trading System, the Brent crude oil market, and the Chinese INE crude oil market. This analysis examined the inter-linkage characteristics between the carbon market and the crude oil market, revealing the patterns of dynamic information spillover between the two markets.