to compare different networks. Therefore, the choice of $p$ which maximizes the signal to noise ratio for each network might not be the best for this purpose. We thus employ the *consistency parameter* $C$, which we calculate for a wide range of $p$ (see Methods for details). This quantity monitors whether the clusterization procedure is accurate and provides a way to consistently compare different networks.

![image](allstructures_4.pdf){width="99.00000%"}

Let us illustrate the behaviour of $C$ for the $N=6$ case in detail as an example (see Fig. \[fig:loyaltyparam\]-b): at $p=1$ only one cluster is present, so $C=1$ by definition. At $p=1.1$ we have 2 clusters, but they are obviously both fully contained in the cluster of the former step, thus $C=1$. The first non trivial value of $C$ is at $p=1.2$ where the 4 clusters are quite well identifiable with the 2 clusters at $p=1.1$. There is a slight drop of $C$, but the value $C=0.99$ is sufficiently close to unity to warrant consistency. This regime is valid up to $p=1.4$, while at $p=1.5$ the value of $C$ drops to $0.95$ (the values of $C$ are normalized); this implies that the clusterization loses some consistency. The biggest drop of $C$ occurs at $p=1.7$, 