How many assumptions are you willing to make? You could grab the two ‘groups’ of edges, and look at their relative positions/orientations/sizes, and best-guess the matching verts/edges from there. For your given example, it wouldn’t be too difficult. The more non-uniform the data gets, the more difficult such an algorithm would be to write (to the point that you’d need to write a more general purpose algorithm altogether). But if it suits your needs, you could start there.
An example algo would go something like:
For a given edge in ‘island 1’ (1A), find all edges of ‘island 2’ that have a similar orientation (normal from edge point 1 to edge point 2).
For each similar edge in island 2, get all the adjacent edges, and sort them according to their normal.
Compare the sorted edges to adjacent edges in island 1’s edge, and choose the island 2 edge that has the most similar matching adjacent edges.
If 2 island 2 edges match equally well, pick the one that is spatially closer.
That edge is the matching ‘bridge’ edge from island 1 edge A to island 2 edge A.
I know such an algorithm would work for many cases, and it could be improved substantially, but that’s a general (and verbose) idea for something that may not work at all for the cases you need it to 