  Deep, classical graph-theoretical parameters, like the size of the minimum
vertex cover, the chromatic number, or the eigengap of the adjacency matrix of
the graph were studied widely by mathematicians in the last century. Most
researchers today study much simpler parameters of braingraphs or connectomes
which were defined in the last twenty years for enormous networks -- like the
graph of the World Wide Web -- with hundreds of millions of nodes. Since the
connectomes, describing the connections of the human brain, typically contain
several hundred vertices today, one can compute and analyze the much deeper,
harder-to-compute classical graph parameters for these, relatively small graphs
of the brain. This deeper approach has proven to be very successful in the
comparison of the connectomes of the sexes in our earlier works: we have shown
that graph parameters, deeply characterizing the graph connectivity are
significantly better in women's connectomes than in men's. In the present
contribution we compare numerous graph parameters in the three largest lobes
--- frontal, parietal, temporal --- and in both hemispheres of the brain. We
apply the diffusion weighted imaging data of 423 subjects of the NIH-funded
Human Connectome Project, and present some findings, never described before,
including that the right parietal lobe contains significantly more edges, has
higher average degree, density, larger minimum vertex cover and Hoffman bound
than the left parietal lobe. Similar advantages in the deep graph connectivity
properties are hold for the left frontal vs. the right frontal and for the
right temporal vs. the left temporal lobes.
