Calculation of the graphene C 1$\textit{s}$ core level binding energy
X-ray photoelectron spectroscopy (XPS) combined with first principles modeling is a powerful tool for determining the chemical composition and electronic structure of novel materials. Of these, graphene is an especially important model system for understanding the properties of other carbon nanomaterials. Here, we calculate the carbon 1$\textit{s}$ core level binding energy of pristine graphene using two methods based on density functional theory total energy differences: a calculation with an explicit core-hole ($\Delta$KS), and a novel all-electron extension of the delta self-consistent field ($\Delta$SCF) method. We study systematically their convergence and computational workload, and the dependence of the energies on the chosen exchange-correlation functional. The $\mathrm{\Delta}$SCF method is computationally more expensive, but gives consistently higher C 1$\textit{s}$ binding energies. Although there is a significant functional dependence, the binding energy calculated using the PBE functional is found to be remarkably close to what has been measured for graphite.