an arbitrarely chosen threshold.

The MST is a correlation based tree associated with the SLCA. An illustrative algorithm providing the MST is the following. Let us first recall that the connected component of a graph $g$ containing the vertex $i$ is the maximal set of vertices $S_i$ (with $i$ included) such that there exists a path in $g$ between all pairs of vertices belonging to $S_i$. When the element $i$ has no links to other vertices then $S_i$ reduces just to the element $i$. The starting point of the procedure is an empty graph $g$ with $N$ vertices. The MST algorithm can be summarized in 6 steps:

1.  Set ${\bf Q}$ as the matrix of elements $q_{ij}$ such that ${\bf Q}={\bf C}$.

2.  Select the maximum correlation $q_{hk}$ between elements belonging to different connected components $S_h$ and $S_k$ in $g$. At the first step of the algorithm connected components coincide with single vertices in $g$.

3.  Find elements $u$, $p$ such that $\rho_{up}=\text{{\bf Max}}\left \{\rho_{ij}, \forall i \in S_h \text{ and } \forall j \in S_k \right \}$

4.  Add to $g$ the link between elements $u$ and $p$ with weight $\rho_{up}$. Once the link is added to $g$, $u$ 