  Network control theory can be used to model how one should steer the brain
between different states by driving a specific region with an input. The needed
energy to control a network is often used to quantify its controllability, and
controlling brain networks requires diverse energy depending on the selected
input region. We use the theory of how input node placement affects the longest
control chain (LCC) in the controllability of brain networks to study the role
of the architecture of white matter fibers in the required control energy. We
show that the energy needed to control human brain networks is related to the
LCC, i.e., the longest distance between the input region and other regions in
the network. We indicate that regions that control brain networks with lower
energy have small LCCs. These regions align with areas that can steer the brain
around the state space smoothly. By contrast, regions that need higher energy
to move the brain toward different target states have larger LCCs. We also
investigate the role of the number of paths between regions in the control
energy. Our results show that the more paths between regions, the lower cost
needed to control brain networks. We evaluate the number of paths by counting
specific motifs in brain networks since determining all paths in graphs is a
difficult problem.
