For networks that are directed or can be represented by a directed networks, reversing one or more of the uni-directional links may provide the ability to reconnect a network that has been disconnected by link failure. In this paper, a new approach to reconfigure such networks is proposed. We develop a linear time algorithm which, when reachability has been destroyed by the removal of a single link, optimally restores reachability through the reversal of selected links. Multi-link failure reconnectability is discussed and an algorithm with polynomial complexity is given which provides a nearly optimum solution to reconnect the network. We show that the reliability of a network that allows reversals is at least twice more than that in which reversals are not permitted. Unfortunately, the reconnection of some networks cannot be established. Therefore, we discuss the maximization of reachability of such networks so that each node can reach maximum number of the other nodes.