  We utilize a model of Wilson-Cowan oscillators to investigate
structure-function relationships in the human brain by means of simulations of
the spontaneous dynamics of brain networks generated through human connectome
data. This allows us to establish relationships between the global excitability
of such networks and global structural network quantities for connectomes of
two different sizes for a number of individual subjects. We compare the
qualitative behavior of such correlations between biological networks and
shuffled networks, the latter generated by shuffling the pairwise
connectivities of the former while preserving their distribution. Our results
point towards a remarkable propensity of the brain's to achieve a trade-off
between low network wiring cost and strong functionality, and highlight the
unique capacity of brain network topologies to exhibit a strong transition from
an inactive state to a globally excited one.
