  The Harper equation arising out of a tight-binding model of electrons on a
honeycomb lattice subject to a uniform magnetic field perpendicular to the
plane is studied. Contrasting and complementary approaches involving von
Neumann entropy, fidelity, fidelity susceptibility, multifractal analysis are
employed to characterize the phase diagram. The phase diagram consists of three
phases: two metallic phases and an insulating phase. A variant model where next
nearest neighbor hopping is included, exhibits a mobility edge and does not
allow for a simple single phase diagram characterizing all the eigenstates.
