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