Near edge x-ray absorption fine-structure spectra of graphenes are calculated using hybrid density-functional theory with the equivalent core hole approximation, aiming to resolve the ongoing debate on the interpretation of corresponding experimental spectra. Effects of size, stacking, edges, and defects on the spectra have been analyzed in detail for both C 1s-π∗ and C 1s-σ∗ transitions. The infinite graphene sheet has been modeled by graphene nanoribbons of different size. The size dependence and convergence of the spectra have been revealed. It is found that the π-π interaction between layers have mainly effects on the C 1s-π∗ transitions in two different energy regions. The stacking effect smears out the double-peaks structure of the first main π∗ peak around 285 eV and results in blueshift of the second π∗ structure by almost 2 eV. The calculations show that the π spectrum of hydrogen saturated edge carbons is redshifted with respect to the central ones and that a new weak σ∗ peak around 288 eV appears. The presence of defects can also introduce new spectral features in both π and σ regions.