I have difficulties finding a good definition of two embeddings of a (planar) graph in the plane being equivalent. Intuitively I mean by equivalent that the embeddings look the same up to homeomorphism of the faces.
The only definition I found was:
Two embeddings of a graph are equivalent if for each vertex all incident edges have the same circular clockwise order in both embeddings.
But this is not strong enough to match my intuitive view, since this notion of equivalence allows connected components to be arbitrarily contained in each other.