one entry for each column is non-zero. Clusters are defined by the connected regions of the percolation network. In the limit of $p=1$, only one cluster is detected. On the other hand, the parameter [*p*]{} is related to the granularity of the clustering process. Large values of [*p*]{} generate several small clusters.

Structural superposition
------------------------

A structural representation of the clusters is obtained in the following way: for each cluster, the most connected structure is taken as reference and all the others are superimposed. For each structure, we represent the one obtained with the combination of labeling, rotation and mirror state which minimizes the similarity parameter $S$ (see [*Network Creation*]{} section). In order to reduce noise, the coordinates of the sites are averaged with the ones from two other structures of the cluster taken at random. Structural rendering is done with VMD [@humphrey1996vmd]. An example of the effects of such algorithm is shown in Fig. \[fig:superimposition\].

We follow this procedure to depict all the clusters in Supp. Fig. \[fig:supp:VMDrepr1\],\[fig:supp:VMDrepr2\],\[fig:supp:VMDrepr3\].

![Distribution of the similarity parameter $S$ for systems with different number of sites. (a) The average similarity between two given structures decreases ($S$ increases) with the number of sites. (b) The 