  We demonstrate that a tight-binding Hamiltonian with nearest- and
next-nearest-neighbor hopping integrals can be decomposed into bulk and
boundary parts in a general lattice system. The Hamiltonian decomposition
reveals that next nearest-neighbor hopping causes sizable changes in the energy
spectrum of surface states even if the correction to the energy spectrum of
bulk states is negligible. By applying the Hamiltonian decomposition to edge
states in graphene systems, we show that the next nearest-neighbor hopping
stabilizes the edge states.
