and $p$ will belong to the same connected component $S=S_h\bigcup S_k$.

5.  Redefine the matrix ${\bf Q}$:

    $$\label{singleadjust}
    \left\{
    \begin{aligned}
    q_{ij} & =q_{hk}, \text{ if } i\in S_h \text{ and } j\in S_k \\
    q_{ij} & =\text{{\bf Max}} \left\{ q_{pt}, p\in S \text{ and } t\in S_j, \text{ with } S_j\neq S \right \}, \\
             & ~~~  \text{ if } i\in S \text{ and } j\in S_j \\
    q_{ij} & =q_{ij}, \text{ otherwise}; \\
    \end{aligned}
    \right.$$

6.  If $G$ is still a disconnected graph then go to step (ii), else stop.\

![ Average linkage cluster analysis. Illustrative example of a hierarchical tree associated to a system of $N=10$ stocks (tick symbols label stocks at the bottom of the hierarchical tree. Each element of the system is also labeled with an integer number). The color of line indicates the primary economic sector of the stock, red for technology, blue for energy and green for financial. The labels of the nodes of the hierarchical tree are used in the discussion of the hierarchically nested factor model of Section \[sectionH\].[]{data-label="dendroALCA"}](HTnyse10_colorEXAMPLE){width="100.00000%"}

![Single linkage cluster analysis. Illustrative example of a hierarchical tree associated to a system of $N=10$ stocks (tick symbols label stocks at the 