  To meet ongoing cognitive demands, the human brain must seamlessly transition
from one brain state to another, in the process drawing on different cognitive
systems. How does the brain's network of anatomical connections help facilitate
such transitions? Which features of this network contribute to making one
transition easy and another transition difficult? Here, we address these
questions using network control theory. We calculate the optimal input signals
to drive the brain to and from states dominated by different cognitive systems.
The input signals allow us to assess the contributions made by different brain
regions. We show that such contributions, which we measure as energy, are
correlated with regions' weighted degrees. We also show that the network
communicability, a measure of direct and indirect connectedness between brain
regions, predicts the extent to which brain regions compensate when input to
another region is suppressed. Finally, we identify optimal states in which the
brain should start (and finish) in order to minimize transition energy. We show
that the optimal target states display high activity in hub regions,
implicating the brain's rich club. Furthermore, when rich club organization is
destroyed, the energy cost associated with state transitions increases
significantly, demonstrating that it is the richness of brain regions that
makes them ideal targets.
