for each structure. In Fig. \[fig:inverseparticip\] the distributions of the maxima of the IPR within $t\in(0,\mathcal{T})$ from $N=4$ to $N=8$ are shown, divided into clusters. Remarkably, the maxima of the IPR spontaneously group into two well defined distributions. The cases $N=4$ and $N=5$ are basically homogeneous, with negligible differences between the two clusters in both systems. The corresponding values lie around $3.3$ and $4.2$, respectively, which means that the excitation is shared between approximately four or five sites. The two values are prototypical for the IPR distributions of clusters with bigger number of sites. In fact, structures in cluster $\tau_6$ have IPR maxima values similar to those in $\tau_a$ and $\tau_b$, while values for structures in $v_6$ have values close to those in $\pi_a$ and $\pi_b$. The distributions for triplet cluster in $N=7$ and the double pair clusters in $N=8$ (red curves) correspond to those for $\tau_a$ and $\tau_b$, while the pair cluster in $N=7$ and the sparse cluster in $N=8$ (blue curves) have the same IPR distribution as $\pi_a$ and $\pi_b$.

Strikingly, the distribution of IPR supports that indeed the backbones of the $\tau_X$ and $\pi_X$ clusters (where $X$ stands for any $N$) for $N>5$ correspond to $\tau_a$/$\tau_b$ and 