Methods and apparatus to determine an alternate route in a network are disclosed. Example methods disclosed herein include processing a label stack of a data packet at a first node to determine whether the data packet is undergoing alternative routing to a destination. Such example methods also include, in response to determining that the data packet is undergoing alternative routing, processing the label stack to determine multiplicity values for neighbor nodes of the first node, respective ones of the multiplicity values representing respective numbers of times the data packet has been routed to respective ones of the neighbor nodes while undergoing alternative routing to the destination. Such example methods further include updating the label stack to increase a respective multiplicity value associated with the first node prior to routing the data packet from the first node to a first one of the neighbor nodes selected based on the multiplicity values.