In this paper, we study the exact learning problem for weighted graphs, where we are given the vertex set, V, of a weighted graph, \(G=(V,E,w)\) , but we are not given E. The problem, which is also known as graph reconstruction, is to determine all the edges of E, including their weights, by asking queries about G from an oracle. As we observe, using simple shortest-path length queries is not sufficient, in general, to learn a weighted graph. So we study a number of scenarios where it is possible to learn G using a subquadratic number of composite queries, which combine two or three simple queries.