a multivariate complex system can be used to extract information about aspects of hierarchical organization of such a system. The clustering procedure is done by using the correlation between pairs of elements as a similarity measure and by applying a clustering algorithm to the correlation matrix. As a result of the clustering procedure, a hierarchical tree of the elements of the system is obtained. The correlation based clustering procedure allows also to associate a correlation based network with the correlation matrix. For example, it is natural to select the minimum spanning tree, i.e. the shortest tree connecting all the elements in a graph, as the correlation based network associated with the single linkage cluster analysis. Different correlation based networks can be associated with the same hierarchical tree putting emphasis on different aspects of the sample correlation matrix. Useful examples of correlation based networks different from the minimum spanning tree are the planar maximally filtered graph (Tumminello et al., 2005) and the average linkage minimum spanning tree (Tumminello et al., 2007c).

In correlation based hierarchical investigations the statistical reliability of hierarchical trees and networks is depending on the statistical reliability of the sample correlation matrix. The sample correlation matrix is computed 