the PMFG (Tumminello et al., 2005). This correlation based network has associated a hierarchical structure which is the one given by SLCA but it presents a graph structure which is richer than the one of the MST. In fact, the PMFG has loops and cliques. A clique of $k$ elements is a complete subgraph that links all $k$ elements. Due to topological constraints, only cliques of 3 and 4 elements are allowed in the PMFG. To illustrate the PMFG algorithm, let us first consider a different construction algorithm for the MST. Following the ordered list $S_{ord}$ of correlation coefficients starting from the couple of elements with largest correlation one adds a link between element $i$ and element $j$ if and only if the graph obtained after the link insertion is still a forest or it is a tree. A forest is a disconnected graph in which any two elements are connected by at most one path, i.e. a disconnected ensemble of trees. With this procedure, equivalent to the algorithm above detailed, the graph obtained after all links of $S_{ord}$ are considered is the MST. In direct analogy, Tumminello et al. (2005) introduce a correlation based graph obtained by connecting elements 