Fig. 2: Genetic influences on connectivity strength are preferentially concentrated on rich-club links.

A Anatomical locations of hubs defined at different levels of k. B The degree distribution of the representative group-level connectome. Mean genetic (C) and unique environmental (D) influences for rich (hub–hub), feeder (hub–nonhub), peripheral (nonhub–nonhub) connections as a function of the hub-defining threshold, k. The mean of the corresponding measure across all network links is shown as a dotted black line. Shaded area corresponds to the standard error of the mean, circles indicate a statistically significant increase of the measure in a given link type compared to the rest of the network (one-sided Welch’s t-test, uncorrected p < 0.05). E Regional assignments to canonical functional network modules³⁸, represented using color. F The proportion of nodes with degree > k in each functional network module as a function of k. G Distributions of heritability estimates across edges within functionally defined networks³⁸: VIS1—primary visual; VIS2—secondary visual; SM—somatomotor; CO—cingulo-opecular; DAN—dorsal attention; LAN—language; FPN—frontoparietal; AUD—auditory; DMN—default mode; PM—posterior multimodal; VM—ventral multimodal; OA—orbito-affective. Rich links within each module are represented as black dots, as defined for k > 105. Heritability distributions for edges within (H) and between (I) functional modules across rich, feeder, and peripheral link types for k > 105. Rich links show significantly higher heritability compared to both feeder and peripheral links, within and between functional modules (one-sided Welch’s t-test, all p < 1.9 × 10⁻¹²). For distributions presented in G–I, 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. Source data are provided as a Source Data file.