the robustness of the observations on a particular data set. In this section, we discuss cut-off choices in some detail.

In Fig. \[fig:Sdistrib\]-a the distributions of $S$ are shown for the most efficient structures ($\epsilon>0.9$) obtained for $N=4-8$. Interestingly, two behaviors are present. The case $N=4$ is compatible with an almost homogeneous ensemble, where any two structures are very similar to each other ($S<0.15$ for the 94% of the links). On the other hand, in the systems with $N=6,7,8$ the number of pairs of compatible structures is instead very small, i.e. the ensemble is deeply heterogeneous ($S>0.15$ for the 92%, 98% and 99% of the links for $N=6,7,8$, respectively). The case $N=5$ shows an intermediate behavior.

![Parameters choice in the clusterization procedure for $N=6$. (a) Relative cluster populations for $p=1.2,1.4,1.6$ are shown in black, dark and light grey, respectively. Significant clusters separate from the noise which results in an exponential tail (fitted dashed lines). (b) Consistency parameter $C$ as a function of $p$.[]{data-label="fig:loyaltyparam"}](consistencyparam_3.pdf){width="47.50000%"}

If only one system is considered, the cut-off needs just to be self consistent, i.e. the results should not vary too much with $S^{*}$. The problem arises when one wishes to compare different networks, [*i.e.*]{} different distance 