The human brain structural network is thought to be shaped by the optimal trade-off between cost and efficiency. However, most studies on this problem have focused on only the trade-off between cost and global efficiency (i.e., integration) and have overlooked the efficiency of segregated processing (i.e., segregation), which is essential for specialized information processing. Direct evidence on how trade-offs among cost, integration, and segregation shape the human brain network remains lacking. Here, adopting local efficiency and modularity as segregation factors, we used a multiobjective evolutionary algorithm to investigate this problem. We defined three trade-off models, which represented trade-offs between cost and integration (dual-factor model), and trade-offs among cost, integration, and segregation (local efficiency or modularity; tri-factor model), respectively. Among these, synthetic networks with optimal trade-off among cost, integration, and modularity (tri-factor model [Q]) showed the best performance. They had a high recovery rate of structural connections and optimal performance in most network features, especially in segregated processing capacity and network robustness. Morphospace of this trade-off model could further capture the variation of individual behavioral/demographic characteristics in a domain-specific manner. Overall, our results highlight the importance of modularity in the formation of the human brain structural network and provide new insights into the original cost-efficiency trade-off hypothesis.

The human brain structural network is hypothesized to be organized under an optimal trade-off between cost and efficiency. However, the efficiency of segregated processing in this trade-off is overlooked. Adopting multiobjective evolutionary algorithm, we revealed that synthetic networks with optimal trade-off among cost, global efficiency, and modularity (tri-factor model [Q]) could capture empirical brain network structure very well. Synthetic networks of tri-factor model (Q) had a high recovery rate of structural connections and optimal performance in network features, especially in segregated processing capacity and network robustness. The morphospace of this model could further capture the variation of individual behavioral/demographic characteristics. These results highlight the indispensable role of modularity in shaping the human brain structural network and provide new insights into the original cost-efficiency trade-off hypothesis.

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Competing Interests: The authors have declared that no competing interests exist.

Handling Editor: Petra Vertes

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