There is substantial evidence to suggest that brain circuits have evolved to be highly efficient and robust while consuming relatively minimal energy. These circuits possess unique structural and functional properties, such as sparsity, complexity, and small-world nature. Studies suggest that brain network development is shaped by a trade-off between minimal wiring cost and efficient communication. However, it is not entirely clear which factors are most influential, and to what extent each factor contributes to this development. Our examination of several potential underlying factors reveals that, with connectivity guaranteed by a fixed degree distribution, minimizing wiring cost has the greatest impact on network structure, compared to factors such as maximizing the clustering coefficient or coefficient of variation for wiring length distribution. While the cost-efficiency balance is capable of optimally reproducing brain networks in five different species without degree constraints, minimizing wiring cost remains the primary determinant.