Rényi indices of financial minimum spanning trees

The Rényi index is used here to describe topological structures of minimum spanning trees (MSTs) of financial markets. We categorize the topological structures of MSTs as dragon, star and super-star types. The MST based on Geometric Brownian motion is of dragon type, the MST constructed by One-Factor Model is super-star type, and most MSTs based on real market data belong to the star type. The Rényi index of the MST corresponding to S&P500 is evaluated, and the result shows that the Rényi index varies significantly in different time periods. In particular, it rose during crises and dropped when the S&P500 index rose significantly. A comparison study between the CSI300 index of the Chinese market and the S&P500 index shows that the MST structure of the CSI300 index varies more dramatically than the MST structure of the S&P500.