Equivalent embeddings of a graph 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.
[Reposting comment as an answer, based on the OP's response to the comment.]

For a combinatorial definition, it seems like what you're looking for is a circular ordering around the vertices together with a map $f$ from the set of components to the set of faces such that $f(C_i)$ is the face of the graph that contains the component $C_i$. 

If you prefer a topological definition, I believe what you're looking for is that the map between the graphs can be extended to a map from the plane to itself that is isotopic to the identity. (Isotopy is, for example, the topological relation typically used to define two knots as being equivalent.)