  It is widely believed that the formation of brain network structure is under
the pressure of optimal trade-off between reducing wiring cost and promoting
communication efficiency. However, the question of whether this trade-off
exists in empirical human brain networks and, if so, how it takes effect is
still not well understood. Here, we employed a multiobjective evolutionary
algorithm to directly and quantitatively explore the cost-efficiency trade-off
in human brain 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 networks but also embed a resembling
small-world structure. 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 attack as the empirical brain networks did.
Additionally, we also revealed some differences of the synthetic networks from
the empirical brain networks, including lower segregated processing capacity
and weaker robustness against targeted attack. 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.
