NEAT algorithm and dynamic topology neural networks
Not an expert in neural net. But I recently read and answer a question on NEAT. From there, I would assume that direction of edges are already determined in each gene. Because of the way operations on genome was designed, I could see that you can ensure the genome is always in `topological order'.

Alternatively, looking at heuristic algorithms that iteratively update graph's weight as it learns (e.g. pagerank and ACO), it should be fine to assume initial weight and just let the iteration stabilise. One could imagine this as every edge being directed both ways --- every link is both input and output.