Cost-efficiency trade-offs of the human brain network revealed by a multiobjective evolutionary algorithm.

It is widely believed that the formation of brain network architecture is under the pressure of optimal trade-off between reducing wiring cost and promoting communication efficiency. However, the questions of whether this trade-off exists in empirical human brain structural networks and, if so, how it takes effect are still not well understood. Here, we employed a multiobjective evolutionary algorithm to directly and quantitatively explore the cost-efficiency trade-off in human brain structural networks. Using this algorithm, we generated a population of synthetic networks with optimal but diverse cost-efficiency trade-offs. It was found that these synthetic networks could not only reproduce a large portion of connections in the empirical brain structural networks but also embed a resembling small-world organization. Moreover, the synthetic and empirical brain networks were found similar in terms of the spatial arrangement of hub regions and the modular structure, which are two important topological features widely assumed to be outcomes of cost-efficiency trade-offs. The synthetic networks had high robustness against random attacks as the empirical brain networks did. Additionally, we also revealed some differences between the synthetic networks and the empirical brain networks, including lower segregated processing capacity and weaker robustness against targeted attacks in the synthetic networks. These findings provide direct and quantitative evidence that the structure of human brain networks is indeed largely influenced by optimal cost-efficiency trade-offs. We also suggest that some additional factors (e.g., segregated processing capacity) might jointly determine the network organization with cost and efficiency.