  In recent years complex networks have gained increasing attention in
different fields of science and engineering. The problem of controlling these
networks is an interesting and challenging problem to investigate. In this
paper we look at the controllability problem focusing on the energy needed for
the control. Precisely not only we want to analyze whether a network can be
controlled, but we also want to establish whether the control can be performed
using a limited amount of energy. We restrict our study to irreducible and
(marginally) stable networks and we find that the leading right and left
eigenvectors of the network matrix play a crucial role in this analysis.
Interestingly, our results suggest the existence of a connection between
controllability and network centrality, a well-known concept in network
science. In case the network is reversible, the latter connection involves the
PageRank, an extensively studied type of centrality measure. Finally, the
proposed results are applied to examples concerning random graphs.
