chosen cutoffs (in grey) show a dependence on N that is similar to that of the average similarity $S$ (in black).[]{data-label="fig:Sdistrib"}](Sdistribuwithcutoffs_2.png){width="47.50000%"}

Consistency parameter $C$ 
--------------------------

In order to monitor whether the clusterization procedure is consistent while varying the granularity parameter $p$, we introduce here a “consistency parameter” $C$. If the clusterization is accurate, an increase in the granularity breaks big clusters into smaller clusters, without mixing them. In fact, every cluster obtained for a given value of $p$ should be fully (or almost fully) included in only one single cluster generated with a smaller value $p -\Delta p$. If this is the case, the clusterization is consistent and the value for $C$ will be maximal. On the other hand, the worst case is a completely random clusterization: the structures of each cluster for a given $p$ are equally distributed between the $n$ clusters generated with $p-\Delta p$. This would correspond to the minimal value of $C$.

For the computation of $C$, we first perform the clusterization analysis from $p=1.1$ to $p=2.2$ in steps of $\Delta p = 0.1$ (from very low to very high values of $p$). For every step $p$, we calculate for each cluster $\mathcal{I}$ the largest portion 