Figure 13.

In-degree distribution for several choices of $k$: The distributions are realized by merging the degree distributions of 1000 different realizations of $\mathcal{O}\mathrm{(100)}$-node graphs. For low values of $k$ (i.e. $k=5$) we see that, for both the H and AF cases, the majority of nodes display rather low in-degree, and the in-degree distribution exhibits a long tail. Conversely, for the CD case, the in-degree is rather homogeneous up to $d_{in}\sim 10$, beyond which the tendency of nodes to acquire more links is softened (apart for a tiny fraction of nodes with $d_{in}\sim 20÷25$). By increasing $k$, nodes with low degree get fewer but still the most predominant for both H and AF patients but new peaks appear in the distribution (see $k=10$) highlighting a change of the topological structure of the network (see also the CD case). This structural change is clear for higher values of $k$ (i.e. $k=20$), especially for H and CD, for which low-linked nodes are fewer, the majority of nodes presenting an in-degree comparable with $k$ ($d_{in}\sim 20÷25$), ultimately suggesting that the networks are becoming regular.