Computational studies considering both thermodynamic and kinetic aspects revealed that graphyne, a carbon material that has recently been of increasing interest, favours unprecedented homogeneous "in-plane" addition reactions. The addition of dichlorocarbene to the C(sp)-C(sp) bond, a site with outstanding regioselectivity in graphyne, proceeds via a stepwise mechanism. Due to their homogeneous nature, additions occurring at C(sp)-C(sp) bonds yield structurally ordered two-dimensional carbon compounds (2DCCs). 2DCCs have electronic band structures near the Fermi level that are similar to those of graphene and are either electrically semi-conductive or metallic depending on whether the reactions break the hexagonal symmetry. Notably, 2DCCs can be further functionalised through substitution reactions with little damage to the extended pi-electron conjugation system. These results suggest that 2DCCs derived from graphyne have physical properties comparable to those of graphene and chemical properties superior to those of graphene. Therefore, 2DCCs are expected to be better suited to practical applications.