Fig. 5.

Empirical versus theoretical probability of connection. Results for UL subject no. 10 are shown. (A) Empirical connection probabilities $p^{\left(l\right)}\left(x_{ij}^{\left(l\right)}\right)$ as a function of the Euclidean distances $x_{ij}^{\left(l\right)}$ in the MH connectome. A, Inset shows the empirical connection probabilities $p^{\left(l\right)}\left(x_{res}^{\left(l\right)}\right)$ as a function of rescaled Euclidean distances $x_{res}^{\left(l\right)}=x^{\left(l\right)}/a^{\left(l\right)}$ with $a^{\left(l\right)}=\left[1.0,1.5,2.6,3.8,4.0\right]$. (B) Empirical versus theoretical connection probability $p^{\left(l\right)}\left({\lambda }_{ij}^{\left(l\right)}\right)$, Eq. 1, in the GR shell. (C) Complementary cumulative degree distribution $P_c\left(k\right)$. (C, Inset) Modularity $Q$, as measured by the Louvain method, is shown. (D) Degree-dependent clustering coefficient $\overline{c}\left(k\right)$. (D, Inset) Average degree of neighbors ${\overline{k}}_{nn,n}\left(k\right)$. The filled symbols correspond to the empirical connectome of subject no. 10. Green dashed lines are generated by using the ${\mathbb{S}}^1$ model with Euclidean distances and parameters $\beta =2.75$ and $\mu =0.0117$. Red lines correspond to the standard ${\mathbb{S}}^1$ model ($\beta =1.96,\mu =0.0104$).