Graph2graph network for geometric shapes

Similar to Seq2Seq models, are there graph2graph models available?

Context: I am working on a dimension reduction problem on shapes, where,

  • shapes are represented as graph,
  • vertices as nodes,
  • connecting curves as edges.
  • dimension reduction operation is called as Midcurve generation.
  • Input is 2D profile, say a closed polygon. Example: thick ‘L’ profile on left in the image below.
  • Output is 1D curve in the middle of the profile. Example: thin ‘L’ curve on the right in the image below

Wish to build encoder-decoder network which accepts graphs as input as well as output.
I have training set of such input and output graphs, a supervised set.

As I could not find ready graph2graph network, I converted the problem to image2image (say, pix2pix like) and then solving it. But wish to investigate if graph2graph network is available or not.

More info:

How to build such encoder decode network? Please note that as both, input and output are different, this can not be AutoEncoder.

Any ideas?