where $C=0.87$ and the consistency of the clusterization process is lost.

For each choice of $N$, $C$ has a different behavior (this can be seen in Fig. \[figsupp:fidelityparam\] in Supp.Mat.). This means that we cannot choose a unique value $p$ to use in all the clusterization processes, but we need to investigate case by case the dependence of $C$ on $p$. We then select the highest value of $p$ for which $C=1$ for a given system size $N$: this systematic choice of $p$ allows a first qualitative understanding of the geometrical characterization of the system. The values correspond to $p=1.3,1.3,1.1,1.1$ for $N=4-7$, respectively. For the case $N=8$, the choice of $p=1.4$ obtained following the mentioned criterion leads to a single cluster. This is probably due to the high value of the $S^{*}$ chosen for this system, which creates a more densely connected network, hard to break into clusters ([*i.e.*]{} a higher value of $p$ would be needed). We therefore increase in this case the value slightly to $p=1.5$.

Results
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Structural characterization of the clusters {#sect:STRCHAR}
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We analyze quantum transport for a large sample ($10^8$) of randomly generated structures with different number of sites ($N=4-8$, see Methods for details). 