of the coordinates of the $i-$th site in the two configurations, and the minimization is performed over all permutations, rotations around the in-out axis and the mirror symmetry. A link is placed in the network only if $S$ lies below a certain threshold value $S^{*}$ which is going to be discussed in detail in the next sections.

![The structural superposition algorithm (here on the first cluster with $N=6$, 10731 structures) makes geometrical features emerge from the noise.[]{data-label="fig:superimposition"}](superimposition_1.pdf){width="47.50000%"}

Network Clusterization
----------------------

Densely connected regions of the network indicate the presence of groups of structures with common geometrical motifs [@Mostarda2013]. We identify these regions using a network clusterization algorithm based on a self-consistency criterion in terms of network random walks, the Markov clusterization algorithm (MCL). The network is in this way split into different clusters comprised of structures with similar sites arrangements [@Gfeller2007; @Van2008]. The method consists of four steps:

(a) start with the transition matrix $A$ of the network, where each column is normalized to 1;

(b) compute $A^{2}$;

(c) take the [*p*]{}-th power ($p>1$) of every element of $A^{2}$, normalize each column;

(d) go back to step (b).

After some iterations of the MCL, $A$ converges to $A_{MCL}$, where only 