A nanoporous carbon framework structure is predicted by combining graph theoretical approaches and density functional calculations. Bond lengths in this polymorph, with all atoms sp(2)-hybridised, are in good agreement with typical C-C and C=C bond lengths, bond angles are close to 120 degrees, and it is 0.36 eV/atom less stable than diamond. The electronic structure suggests it is a quasi-one-dimensional metal with anisotropic electronic properties and a spectroscopic signature. The compound has a high bulk modulus of 234(1) GPa but a density similar to that of graphite and amorphous carbon. Changes in the lattice parameters on compression are strongly anisotropic.