There are algorithms that will directly enumerate non-isomorphic graphs, without duplicates, e.g. geng available as a part of nauty and it also have procedures to generate non-isomorphic digraphs with a fixed underlying graph, one is directg (see chapter 15 of nauty manual

There are algorithms that will directly enumerate non-isomorphic graphs, without duplicates, e.g. geng available as a part of nauty and it also have procedures to generate non-isomorphic digraphs with a fixed underlying graph, one is directg (see chapter 15 of nauty manual)

Edit: nauty also have various convenient interfaces, e.g. from Python (SageMath and pynauty)