and by applying a given hierarchical clustering procedure, we first obtain a hierarchical tree. The information present in the hierarchical tree is completely equivalent to the information stored in the filtered matrix and, when the correlation is non-negative for each pair of elements, this matrix is positive definite (Tumminello et al., 2007d).

Our example considers the correlation matrix of $N=10$ daily stock returns traded at the New York Stock Exchange during the time period from January 2001 to December 2003. The investigated stocks are AIG, IBM, BAC, AXP, MER, TXN, SLB, MOT, RD, and OXY. The above presentation order of stocks is given according to their market capitalization at December 2003. In this paper, we indicate stocks with their tick symbols. The tick symbol, company name and other information of each company are given in Table I. From the Table we note that three stocks (OXY, RD, SLB) belong to the energy sector, three (IBM, MOT, TXN) to the technology sector and four (AIG, AXP, BAC, MER) to the financial sector.

The stock return correlation matrix computed by using $T=748$ records is the following $$\label{corrmat}
{\bf C}=\left(
\begin{array}{cccccccccc}
1.000   &   0.413   &   0.518   &   0.543   &   0.529   &   0.341   &   