  Selecting appropriate inputs for systems described by complex networks is an
important but difficult problem that largely remains open in the field of
control of networks. Recent work has proposed two methods for energy efficient
input selection; a gradient based heuristic and a greedy approximation
algorithm. We propose here an alternative method for input selection based on
the analytic solution of the controllability Gramian of the `balloon graph', a
special model graph that captures the role of both \emph{distance} and
\emph{redundant paths} between a driver node and a target node. The method
presented is especially applicable for large networks where one is interested
in controlling only a small number of outputs, or target nodes, for which
current methods may not be practical because they require computing a typically
very ill-conditioned matrix, called the controllability Gramian. Our method
produces comparable results to the previous methods while being more
computational efficient.
