  X-ray photoelectron spectroscopy of graphene is important both for its
characterization and as a model for other carbon materials. Despite great
recent interest, the intrinsic photoemission of its single layer has not been
unambiguously measured, nor is the layer-dependence in free-standing
multilayers accurately determined. We combine scanning transmission electron
microscopy and Raman spectroscopy with synchrotron-based scanning photoelectron
microscopy to characterize the same areas of suspended graphene samples down to
the atomic level. This allows us to assign spectral signals to regions of
precisely known layer number and purity. The core level binding energy of the
monolayer is measured at 284.70 eV, thus 0.28 eV higher than that of graphite,
with intermediate values found for few layers. This trend is reproduced by
density functional theory with or without explicit van der Waals interactions,
indicating that intralayer charge rearrangement dominates, but in our model of
static screening the magnitudes of the shifts are underestimated by half.
