I have this very specific problem and I didn't find anything searching, so I apologize if the question is trivial. Also, graph theory is not really my thing so I could miss important points.
That being said, I have the following problem. I have a directed graph $G_1$, with $N$ nodes, completely connected, so with $2N^2$ edges. Each edge has a cost assigned to it. I have complete knowledge of this graph, so I know all nodes, edges and costs. Then, I have a second graph $G_2$ which has the same nodes and edges, but with different costs which are only partially known. My objective is to estimate the costs of edges in $G_2$. I assume there is some kind of correlation between the costs of edges in $G_1$ and $G_2$, which I would like to take into account in the cost estimation.
Of course, the trivial case is the one in which I have no knowledge of $G_2$. In this case, the only reasonable thing would be to assign the same costs I observe in $G_1$ to the edges. Suppose now that I observe the real values of an edge of $G_2$. I would like to adapt my expectation of the other costs considering this new observation.
Is there some well-known algorithm for this "paired graph" problem that I am missing, or any resource that could help me?
Thanks in advance.