The Graph of Our Mind.

Graph theory in the last two decades penetrated sociology, molecular biology, genetics, chemistry, computer engineering, and numerous other fields of science. One of the more recent areas of its applications is the study of the connections of the human brain. By the development of diffusion magnetic resonance imaging (diffusion MRI), it is possible today to map the connections between the 1-1.5 cm2 regions of the gray matter of the human brain. These connections can be viewed as a graph. We have computed 1015-vertex graphs with thousands of edges for hundreds of human brains from one of the highest quality data sources: the Human Connectome Project. Here we analyze the male and female braingraphs graph-theoretically and show statistically significant differences in numerous parameters between the sexes: the female braingraphs are better expanders, have more edges, larger bipartition widths, and larger vertex cover than the braingraphs of the male subjects. These parameters are closely related to the quality measures of highly parallel computer interconnection networks: the better expanding property, the large bipartition width, and the large vertex cover characterize high-quality interconnection networks. We apply the data of 426 subjects and demonstrate the statistically significant (corrected) differences in 116 graph parameters between the sexes.