Can't offer a complete solution, but it looks related to the travelling salesman problem where the unknown edges are the nodes to be visited.
You can create a second graph, G', which will be the same - but without the "unkown edges"1. Then, you can use all to all shortest path algorithm, and use the data from the algorithm to fill in the blanks.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.