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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 cm$^2$ regions of the gray matter of the human brain. These connections can be viewed as a graph: the vertices are the anatomically identified regions of the gray matter, and two vertices are connected by an edge if the diffusion MRI-based workflow finds neuronal fiber tracts between these areas. This way we can compute 1015-vertex graphs with tens of thousands of edges. In a previous work, we have analyzed the male and female braingraphs graph-theoretically, and we have found 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. Our previous study has applied the data of 96 subjects; here we present a much larger study of 426 subjects. Our data source is an NIH-founded project, the "Human Connectome Project (HCP)" public data release. As a service to the community, we have also made all of the braingraphs computed by us from the HCP data publicly available at the \url{http://braingraph.org} for independent validation and further investigations.