  We show that the electron-phonon coupling strength obtained from the slopes
of the electronic energy vs. wavevector dispersion relations, as often done in
analyzing angle-resolved photoemission data, can differ substantially from the
actual electron-phonon coupling strength due to the curvature of the bare
electronic bands. This effect becomes particularly important when the Fermi
level is close to a van Hove singularity. By performing {\it ab initio}
calculations on doped graphene we demonstrate that, while the apparent strength
obtained from the slopes of experimental photoemission data is highly
anisotropic, the angular dependence of the actual electron-phonon coupling
strength in this material is negligible.
