  Graphene, a two dimensional (2D) carbon sheet, acquires many of its amazing
properties from the Dirac point nature of its electronic structures with
negligible spin-orbit coupling. Extending to 3D space, graphene networks with
negative curvature, called Mackay-Terrones crystals (MTC), have been proposed
and experimentally explored, yet their topological properties remain to be
discovered. Based on the first-principle calculations, we report an all-carbon
MTC with topologically non-trivial electronic states by exhibiting node-lines
in bulk. When the node-lines are projected on to surfaces to form circles,
"drumhead" like flat surface bands nestled inside of the circles are formed.
The bulk node-line can evolve into 3D Dirac point in the absence of inversion
symmetry, which has shown its plausible existence in recent experiments.
