  We consider the 1015-vertex human consensus connectome computed from the
diffusion MRI data of 1064 subjects. We define seven different orders on these
1015 graph vertices, where the orders depend on parameters derived from the
brain circuitry, that is, from the properties of the edges (or connections)
incident to the vertices ordered. We order the vertices according to their
degree, the sum, the maximum, and the average of the fiber counts on the
incident edges, and the sum, the maximum and the average length of the fibers
in the incident edges. We analyze the similarities of these seven orders by the
Spearman correlation coefficient and by their inversion numbers and have found
that all of these seven orders have great similarities. In other words, if we
interpret the orders as scoring of the importance of the vertices in the
consensus connectome, then the scores of the vertices will be similar in all
seven orderings. That is, important vertices of the human connectome typically
have many neighbors, connected with long and thick axonal fibers (where
thickness is measured by fiber numbers), and their incident edges have high
maximum and average values of length and fiber-number parameters, too.
Therefore, these parameters may yield robust ways of deciding which vertices
are more important in the anatomy of our brain circuitry than the others.
