participants the list of all connections, the degrees of their stubs ( k$_{u}$ and k$_{v}$ ), and length ( E ( u, v )). From these data, we estimated the three-dimensional cumu- lative distribution function, F ( k$_{α}$, k$_{β}$, E ( α, β )). At any point { k$_{α}$, k$_{β}$, E ( α, β ) } , the value of F corresponded to the fraction of all connections satisfying k$_{u}$ ≤ k$_{α}$ , k$_{v}$ ≤ k$_{β}$ , and E ( u, v ) ≤ E ( α, β ) ( k$_{u}$ and k$_{v}$ were ordered so that k$_{u}$ ≤ k$_{v}$ ). We constructed similar distributions for the best-fitting synthetic networks gener- ated by each model and quantified the discrepancy between distributions with a KS statistic. In general, the rank order of models scored by this KS statistic was similar to the rank order of their energies (Figure 4B). The MI model achieved the smallest KS statistic ( KS = 0 . 12 ± 0 . 01) while the pure geometric model, on the other hand, performed the worst ( KS = 0 . 37 ± 0 . 01). 

## 3.3.3. Local statistics 

Finally, we tested whether the best-fitting synthetic networks generated by the MI model were capable of predicting the degree and clustering coefficient sequences of the connectome. We expressed each node’s empirical degree, k$_{u}$ , and clustering coefficient, c$_{u}$ , as z-scores by standardizing the empirical values against the distributions obtained from the best-fitting synthetic networks. Z- scores were averaged across subjects and used to quantify the discrepancy in those measures (larger scores indicated poorer fit). We compared these z-scores against scores obtained from the best-fitting synthetic networks generated by the pure geometric model in order to ascertain whether they represented an improvement in fitting local network measures (Figure 4C). We found that, on average, the MI model produced smaller discrepancies (points below the diag- onal) compared to the geometric model. Typically, the largest improvements were for nodes whose degree or clustering coefficient was mismatched the great- est by the geometric model. For some nodes, however, the geometric model actually outperformed the MI model, though the standardized scores for these 

