Consider two data holders, ABC and XYZ, with graph data (e.g., social networks, e-commerce, telecommunication, and bio-informatics). ABC can see that node A is linked to node B, and XYZ can see node B is linked to node C. Node B is the common neighbour of A and C but neither network can discover this fact on their own. In this paper, we provide a two party computation that ABC and XYZ can run to discover the common neighbours in the union of their graph data, however neither party has to reveal their plaintext graph to the other. Based on private set intersection, we implement our solution, provide measurements, and quantify partial leaks of privacy. We also propose a heavyweight solution that leaks zero information based on additively homomorphic encryption.