Atomic correlation between adjacent graphene layers was elucidated for double-wall carbon nanotubes (DWNTs) through a chiral index assignment of two nested nanotubes by high-resolution transmission electron microscopy. Our analysis provides a rather constant diameter difference close to 0.75 nm but no chiral angle correlation between the constituent nanotubes in the concentric DWNTs. The local atomic correlation as a commensurate graphene stacking was repeatedly found in eccentric DWNTs and circumscribed nanotubes, which should lead to elastic deformation and bundling of nanotubes.