A method is provided in one example embodiment and includes receiving a first pseudo-node identifier associated with a first network node via a network. The first pseudo-node identifier is generated by the first network node in a first designated intermediate system (DIS) operation. The method further includes detecting a loss of connectivity to the first network node, and receiving a second pseudo-node identifier associated with a second network node via the network. The second pseudo-node identifier is generated by the second network node in a second DIS operation. The method further includes executing a first network path determination operation using the first pseudo-node identifier and the second pseudo-node identifier when an elapsed time between the detecting of the loss of connectivity with the first network node and the executing of the first network path determination operation is within a predetermined threshold.