Methods, apparatus and articles of manufacture (e.g., physical storage media) to perform centralized route determination in communication networks (e.g., such as software defined networks) are disclosed. Example methods for route determination disclosed herein include accessing, with a controller of a software defined network, a first set of constraints specifying whether route splitting is permissible for respective ones of a set of flows in the software defined network. Such disclosed example methods also include accessing, with the controller, a second set of constraints specifying respective bandwidth demands for the respective ones of the set of flows in the software defined network. Such disclosed example methods further include determining, with a linear programming model implemented by the controller, a set of routes based on the first and second sets of constraints, wherein the set of routes is to route the set of flows in the software defined network.