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We study the time dependence of maximal spanning trees and asset graphs basedon correlation matrices of stock returns. In these networks the nodes representcompanies and links are related to the correlation coefficients between them.Special emphasis is given to the comparison between ordinary and denoisedcorrelation matrices. The analysis of single- and multi-step survival ratios ofthe corresponding networks reveals that the ordinary correlation matrices aremore stable in time than the denoised ones. Our study also shows that someinformation about the cluster structure of the companies is lost in thedenoising procedure. Cluster structure that makes sense from an economic pointof view exists, and can easily be observed in networks based on denoisedcorrelation matrices. However, this structure is somewhat clearer in thenetworks based on ordinary correlation matrices. Some technical aspects, suchas the random matrix denoising procedure, are also presented.

Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks