where the arguments are Kolmogorov-Smirnov statistics which quantify the dis- crepancy between the synthetic and observed connectomes in terms of their degree ( k ), clustering ( c ), betweenness centrality ( b ), and edge length ( e ) distri- butions. Here, edge length refers to the Euclidean distance between the centroids of two connected brain regions. By taking the maximum of the four statistics we consider a synthetic network to be only as fit as its greatest discrepancy. 

## 2.4. Model optimization 

Given the generative rule and the energy measure for evaluating a model network’s goodness of fit, it was important to find the parameters { η, γ } that produced networks with the lowest possible energy values. To solve this opti- mization problem, we developed a simple procedure based on classical Monte Carlo methods. The procedure consisted of three stages that were repeated: 

1. A sampling stage in which points in parameter space are selected 

2. An evaluation stage, where synthetic networks are generated with the previously-selected parameter values and their energies calculated. 

3. A partitioning stage, in which the entire parameter space is partitioned according to a Voronoi tessellation. 

The procedure is initialized in stage 1 by randomly sampling N$_{samp}$ = 2000 points from parameter space. After evaluating the energy at each point and partitioning the entire parameter space into Voronoi cells, the algorithm returns to stage 1. Rather than sample points randomly, points are now sampled from within the boundaries of Voronoi cells, where the probability of drawing a point from within any given cell is inversely proportional to that cell’s energy ( P ( C ) ∝ E − α C , where E$_{C}$ is the energy of Voronoi cell, C , and P ( C ) is the relative probability of sampling from within that cell). This procedure ensures that points are sampled preferentially from low-energy regions of parameter space. 

