Fig. 4: Generative brain network models do not reproduce the spatial topography of brain network hubs.

A Each distribution represents estimates of model fit, as quantified by the maximum KS value of the top 100 networks (out of 10,000) produced by the model optimization procedure. The color of each box indicates conceptually related models, as determined by the specific topology metric used in the model [Table 2]. White dots represent median values for each distribution. The interquartile range is represented with a dark gray box, whiskers are represented with a light gray line. Models favoring homophilic connectivity between node pairs are shown in red, those favoring clustering in orange, those based on the degree in light blue, and a purely spatial model considering wiring costs alone is in dark blue. The specific wiring-rule names are shown along the horizontal axis, with formal definitions provided in Table 2. Cumulative distributions of: B node degree, k; C betweenness centrality, b; D clustering coefficient, c; and E edge length, d, for the empirical connectome (darker line) and 100 runs (lighter lines) of the best-fitting “deg-avg” model corresponding to the data points shown in A. F Anatomical locations of hubs defined for a single hemisphere at selected k thresholds for the empirical data (top) and the single run of the optimized “deg-avg” generative model demonstrating the best model fit across 10,000 runs (bottom). G Correlation between the degree sequences of the empirical data and the best-fitting generative model within a single hemisphere (Spearman’s ρ = −0.05, p = 0.49). H The distribution of correlation values quantifying the relationship between left hemisphere degree sequences of the empirical data and synthetic networks generated using the top 100 best-fitting parameter combinations for each of the 13 considered models, corresponding to the data points shown in A. Source data are provided as a Source Data file.