Machine learning on graphs

I’m looking for some method/model to help me with my current problem:

I have a geometry, consisting of points, and eges. For each point I take information about itself and its neighbours. For now I put these information inside a vector, which works as feature set. all of the info are continuous values.

Then, my target can intuitively be seen as another type of information of geometry regarding the same node for which we extract the info. Also the target is represented as a vector.

For now I had my Deep NN working on this kind of training set, where each example consist of (info on some node_i, relative target). Thus, the NN performs a multi-target regression

The problem now is that this kind of model can work if I have only the same amount of information both for features and target. Seeing it again in the geometry, it only works with nodes which have the same fixed number of neighbors.

Now, I would like to generalize this model, accepting also nodes with less neighbors, which would give rise to less features and also less target values.

To stay inside the geometry example, if you think about a chessboard, my model works for internal nodes, having always 4 neighbors, but if I am on the boundary this cannot work anymore.

For these reason, I started to study Graph neural networks, since we can see our geometry as a graph with nodes and edges.

But it is not clear to me if I can use a training set where each example is itself a graph. Furthermore, I’m not sure it could solve the problem of the fixed-dimension constraint.

Is there any model or method or preprocessing which can suit my acutal problem?