In this case, increasing $p$ to $1.4$ separates this cluster into $7$ smaller more homogeneous clusters, with sites either disposed on a line or in a sparse manner. A more detailed discussion of the case $N=6$ can be found in [@Mostarda2013]. Also the second cluster $v_8$ for $N=8$ (36.9% of the population) is poorly identifiable. Cluster $v_8$ is in fact composed by a well defined backbone-like module with five sites and the remaining three sites in a sparse configuration. With the chosen granularity value $p=1.5$, the latter module is not compatible with a triplet. Subgroups at higher $p$, but with a very small population, present a triplet in a similar manner as in $\tau_7$.

Altogether these results provide evidence for the presence of a modular arrangement in the geometries of efficient structures.

Inverse participation ratio
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So far, we have constructed and clusterized a complex network of efficient structures on purely geometrical grounds. Now we move to investigate the dynamics of these structures, to better understand whether the common geometrical features identified correspond to dynamical similarities.

To quantitatively characterize the dynamical behavior of the identified structures, the inverse participation ratio (IPR, see Methods) is calculated at every instant of time 