The Riemannian positive mass theorem and its rigidity is recently proven for asymptotically flat hypersurfaces in Euclidean space in all dimensions. The rigidity says that the hyperplane is the only asymptotically flat hypersurface with nonnegative scalar curvature whose ADM mass is zero. In this talk, we consider a class of asymptotically flat graphs with small positive mass and show that the graph is effectively close to a hyperplane if the mass is small. This is a joint work with Dan Lee.