  Following up on the recent work of Cachazo, He and Yuan
\cite{arXiv:1503.04816 [hep-th]}, we derive the double soft graviton theorem in
perturbative gravity. We show that the double soft theorem derived using CHY
formula precisely matches with the perturbative computation involving Feynman
diagrams. In particular, we find how certain delicate limits of Feynman
diagrams play an important role in obtaining this equivalence.
