  Edge states in topological insulators (TIs) disperse symmetrically about one
of the time-reversal invariant momenta $\Lambda$ in the Brillouin zone (BZ)
with protected degeneracies at $\Lambda$. Commonly TIs are distinguished from
trivial insulators by the values of one or multiple topological invariants that
require an analysis of the bulk band structure across the BZ. We propose an
effective two-band Hamiltonian for the electronic states in graphene based on a
Taylor expansion of the tight-binding Hamiltonian about the time-reversal
invariant $M$ point at the edge of the BZ. This Hamiltonian provides a faithful
description of the protected edge states for both zigzag and armchair ribbons
though the concept of a BZ is not part of such an effective model. We show that
the edge states are determined by a band inversion in both reciprocal and real
space, which allows one to select $\Lambda$ for the edge states without
affecting the bulk spectrum.
