  We study free graviton entanglement between Rindler wedges in the Minkowski
vacuum state via the Euclidean path integral. We follow Kabat's method for
computing the conical entropy, using the heat kernel on the cone with the tip
removed, whose resulting von Neumann entropy for photons correctly predicted
electromagnetic edge modes. We find that, in addition to the bulk graviton
contributions, the conical entropy has a contact term that can be attributed to
a vector field anchored to the (d-2)-dimensional (Euclidean) Rindler horizon
whose contribution equals d-2 times Kabat's contact term for photons. We
suggest that graviton edge modes are hence the d-2 large diffeomorphisms which
act internally within the Rindler horizon. Along the way, we address several
known issues regarding graviton entanglement. We furthermore sketch how our
results may be used to study edge modes in closed bosonic string theory.
