the same in terms of hierarchical tree. This degeneracy allows one to consider different rules to select the link between elements $u$ and $p$ at the step (iii) of the construction algorithm. Different rules at step (iii) give rise to different correlation based trees. The same observation holds true for the algorithm that generates the MST. This fact implies that in principle one can consider spanning trees which are different from the MST and are still associated with the SLCA. However, we have already recalled that the MST is unique in the sense that, when an Euclidean distance is defined between links of the spanning tree, MST is the spanning tree of shortest length (West, 2001).

For the present example the ALMST is essentially indistinguishable from the MST and for this reason we will not display it here. It is worth noting that whereas the hierarchical trees obtained with ALCA and SLCA show slight differences, these differences essentially disappears at the level of the associated correlation based trees in the present example.

Starting from the sample correlation matrix one can also obtain correlation based networks having a structure more complex than a tree. One of such correlation based networks is 