  We present a two-band model based on periodic H\"uckel theory, which is
capable of predicting the existence and position of Dirac cones in the first
Brillouin zone of an infinite class of two-dimensional periodic carbon
networks, obtained by systematic perturbation of the graphene connectivity by
bond decoration, that is by inclusion of arbitrary $\pi$-electron H\"uckel
networks into each of the three carbon-carbon $\pi$-bonds within the graphene
unit cell. The bond decoration process can fundamentally modify the graphene
unit cell and honeycomb connectivity, representing a simple and general way to
describe many cases of graphene chemical functionalization of experimental
interest, such as graphyne, janusgraphenes and chlorographenes. Exact
mathematical conditions for the presence of Dirac cones in the spectrum of the
resulting two-dimensional $\pi$-networks are formulated in terms of the
spectral properties of the decorating graphs. Our method predicts the existence
of Dirac cones in experimentally characterized janusgraphenes and
chlorographenes, recently speculated on the basis of DFT calculations. For
these cases, our approach provides a proof of the existence of Dirac cones, and
can be carried out at the cost of a back of the envelope calculation, bypassing
any diagonalization step, even within H\"uckel theory.
