  The Chalker-Coddington network model (introduced originally as a model for
percolation in the quantum Hall effect) is known to map onto the
two-dimensional Dirac equation. Here we show how the network model can be used
to solve a scattering problem in a weakly doped graphene sheet connected to
heavily doped electron reservoirs. We develop a numerical procedure to
calculate the scattering matrix with the aide of the network model. For
numerical purposes, the advantage of the network model over the honeycomb
lattice is that it eliminates intervalley scattering from the outset. We avoid
the need to include the heavily doped regions in the network model (which would
be computationally expensive), by means of an analytical relation between the
transfer matrix through the weakly doped region and the scattering matrix
between the electron reservoirs. We test the network algorithm by calculating
the conductance of an electrostatically defined quantum point contact and
comparing with the tight-binding model of graphene. We further calculate the
conductance of a graphene sheet in the presence of disorder in the regime where
intervalley scattering is suppressed. We find an increase in conductance that
is consistent with previous studies. Unlike the tight-binding model, the
network model does not require smooth potentials in order to avoid intervalley
scattering.
