the correlation matrix among $n$ elements of interest. A complete graph is too rich of information and therefore a “filterin” (or “pruning”) of it can improve its readability. For this reason a procedure can be set to select a subset of links which are highly informative about the hierarchical structure of the system. By using clastering algorithms as filtering procedures a certain number of correlation based graphs have been investigated in the econophysics literature. Correlation based networks which have been found very useful in the elucidation of economic properties of stock returns traded in a financial market are the minimum spanning tree (MST) (Mantegna, 1999), the planar maximally filtered graph (PMFG) (Tumminello et al., 2005) and the average linkage minimum spanning tree (ALMST) (Tumminello et al., 2007c). In the cited cases all the elements of the system are connected within the graph. Correlation based graphs with elements disconnected from a giant component can also be obtained starting from the correlation matrix. For example, an extension from trees to more general graphs generated by selecting the most correlated links has been proposed in Onnela et al. (2003). However, this last method selects only a subset of the investigated elements controlled by 