Fig. 6: Graph properties of highlighted subgraphs derived from the top 5% of edges from two pathways in the ABCD dataset.

a, b Node degree distribution of subgraphs for GAT and LM pathways. The GAT-induced subgraph exhibits a skewed distribution with a few highly connected hubs, indicative of a scale-free network, often associated with the brain’s robustness and resilience to localized failures. The LM-induced subgraph exhibits a broader distribution with a higher concentration of nodes having intermediate degrees, reflecting the distributed processing across multiple brain regions. c Comparison between other numerical graph properties. The GAT-induced subgraph demonstrates higher clustering coefficients and modularity, indicating tightly-knit communities and clear modular divisions. Additionally, the small-worldness metric is significantly higher, suggesting an optimal balance between local specialization and global integration. In contrast, the LM-induced subgraph features shorter average path lengths and higher global efficiency, reflecting a network structure optimized for rapid information transfer. Besides, the higher assortativity coefficient in the LM subgraph points to stronger connections between functionally similar brain regions.