Table 1.

Breaking vectors and intertwining indices.

${\mathcal{B}}_1^5=\left[{\overbrace{{\underbrace{a}}_{C_1^5}{\underbrace{b}}_{C_4^5}}}^{C_1}{\overbrace{000}}^{C_2}\right]$	$n_1^5=1$
${\mathcal{B}}_1^6=\left[{\underbrace{a}}_{C_1^6}{\underbrace{b}}_{C_2^6}000\right]$	$n_1^6=1$
${\mathcal{B}}_2^1=\left[00{\underbrace{a}}_{C_3^1}{\underbrace{bb}}_{C_2^1}\right]$	$n_2^1=0$
${\mathcal{B}}_2^2=\left[00{\underbrace{aa}}_{C_2^2}{\underbrace{b}}_{C_3^2}\right]$	$n_2^2=0$
${\mathcal{B}}_2^3=\left[00aba\right]$	$n_2^3=0$
${\mathcal{B}}_2^4=\left[00abc\right]$	$n_2^4=0$
${\mathcal{B}}_2^5=\left[00aba\right]$	$n_2^5=1$
${\mathcal{B}}_2^6=\left[00abc\right]$	$n_2^6=1$

Breaking vectors ${\mathcal{B}}_q^j$ and corresponding intertwining indices $n_q^j$ for each partition ${\mathcal{P}}^j$ and for the equitable clusters C₁ and C₂ of the network of Fig. 2, partition $\mathcal{P}$. For the first four breaking vectors also the broken clusters are shown. Cluster C₁ is broken only in partitions ${\mathcal{P}}^5$ and ${\mathcal{P}}^6$ (see the first two rows and Fig. 2). In ${\mathcal{P}}^5$ (see Fig. 2), C₁ is broken as described in the first row (${\mathcal{B}}_1^5$) and also C₂ is broken, therefore $n_1^5=1$. Cluster C₂ is broken in all partitions. In particular, in ${\mathcal{P}}^1$ cluster, C₂ is broken as described in the third row (${\mathcal{B}}_2^1$) while cluster C₁ is not broken (see Fig. 2), therefore $n_2^1=0$.