  We study how to construct Dirac fermion defined on the honeycomb lattice in
position space. Starting from the nearest neighbor interaction in tight binding
model, we show that the Hamiltonian is constructed by kinetic term and second
derivative term of three flavor Dirac fermions in which one flavor has a mass
of cutoff order and the other flavors are massless. In this formulation the
structure of the Dirac point is simplified so that its uniqueness can be easily
shown even if we consider the next-nearest neighbor interaction. We also show
the chiral symmetry at finite lattice spacing, which protects the masslessness
of the Dirac fermion, and discuss the analogy with the staggered fermion
formulation.
