  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.
