Random Research highlight: Comparison of the braingraphs of the sexes: We have examined braingraphs, computed from the data of the Human Connectome Project, recorded from male and female subjects between ages 22 and 35. Significant differences were found between the male and female structural braingraphs: we show that the average female connectome has more edges, is a better expander graph, has larger minimal bisection width, and has more spanning trees than the average male connectome. Since the average female brain weights less than the brain of males, these properties show that the female brain has better graph theoretical properties, in a sense, than the brain of males. We have also found that the minimum bisection width, normalized with the edge number, is also significantly larger in the right and the left hemispheres in females: therefore, the differing bisection widths are independent from the difference in the number of edges. PLoS One, 10(7): e0130045. doi:10.1371/journal.pone.0130045.