A Bi-directional Link Self-healing Network (BLSN) for implementing bi-directional link automatic protection switching (APS) for an arbitrary edge or node redundant network and a technique for implementing APS recovery in response to an edge or node failure in a network is described. The BLSN technique does not require permanent allocation of spare capacity for each connection and allows sharing of capacity among many network connections by allocating capacity for use only in the event of a failure. The described technique allows loopback protection to be performed over node or edge redundant networks and operates such that the remains connected after the failure of a node or an edge in the network. The technique makes use of connected directed subgraphs of the network. Also described are techniques for generating the directed subgraphs on node and edge redundant networks having an arbitrary network topology.