  We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric
tight-binding ring with an onsite energy $a$ at the gain and loss sites. We
show that if $a\neq 0$, the system generically exhibits an unbroken
$\mathcal{PT}$-symmetric phase. We study the nature of the spectrum in terms of
the singularities in the complex parameter space as well as the behavior of the
eigenstates at large values of the gain and loss strength. We find that in
addition to the usual exceptional points, there are "diabolical points", and
inverse exceptional points at which complex eigenvalues reconvert into real
eigenvalues. We also study the transport through the system. We calculate the
total flux from the source to the drain, and how it splits along the branches
of the ring. We find that while usually the density flows from the source to
the drain, for certain eigenstates a stationary "backflow" of density from the
drain to the source along one of the branches can occur. We also identify two
types of singular eigenstates, i.e. states that do not depend on the strength
of the gain and loss, and classify them in terms of their transport properties.
