  In order to understand the complex cognitive functions of the human brain, it
is essential to study the structural connectome, i.e., the wiring of different
brain regions to each other through axonal pathways. However, the high degree
of plasticity and cross-population variability in human brains makes it
difficult to relate structure to function, motivating a search for invariant
patterns in the connectivity. At the same time, variability within a population
can provide information about generative mechanisms. In this paper we analyze
the connection topology and link-weight distribution of human structural
connectomes obtained from a database comprising 196 subjects. By demonstrating
a correspondence between the occurrence frequency of individual links and their
average weight across the population, we show that the process by which the
brain is wired is not independent of the process by which the link weights of
the connectome are determined. Furthermore, using the specific distribution of
the weights associated with each link over the entire population, we show that
a single parameter that is specific to a link can account for its frequency of
occurrence, as well as, the variation in its weight across different subjects.
This parameter provides a basis for ``rescaling'' the link weights in each
connectome, allowing us to obtain a generic network representative of the human
brain, distinct from a simple average over the connectomes. We obtain
functional connectomes by implementing a neural mass model on each of the
vertices of the corresponding structural connectomes. By comparing with the
empirical functional brain networks, we demonstrate that the rescaling
procedure yields a closer structure-function correspondence. Finally, we show
that the representative network can be decomposed into a basal component that
is stable across the population and a highly variable superstructure.
