  We have performed the comparative spectral analysis of structural connectomes
for various organisms using open-access data. Our analysis indicates several
new peculiar features of the human connectome. We found that the spectral
density of human connectome has the maximal deviation from the spectral density
of the randomized network compared to all other organisms. For many animals
except human structural peculiarities of connectomes are well reproduced in the
network evolution induced by the preference of 3-cycles formation. To get the
reliable fit , we discovered the crucial role of the conservation of local
clusterization in human connectome evolution. We investigated for the first
time the level spacing distribution in the spectrum of human connectome graph
Laplacian. It turns out that the spectral statistics of human connectome
corresponds exactly to the critical regime familiar in the condensed matter
physics which is hybrid of Wigner-Dyson and Poisson distributions. This
observation provides the strong support for the much debated statement of the
brain criticality.
