3D architectures constructed from a tubular graphene network can withstand repeated > 95% compression cycling without damage. Aided by intertubular covalent bonding, this material takes full advantage of the graphene tube's unique attributes, including complete pre- and post-buckling elasticity, outstanding electrical conductivity, and extraordinary physicochemical stability. A highly connected tubular graphene will thus be the ultimate, structurally robust, ultrastrong, ultralight material.