Brain matching is an important problem in neuroimaging studies. Current surface-based methods for cortex matching and atlasing, although quite accurate, can require long computation times. Here we propose an approach based on spectral correspondence, where spectra of graphs derived from the surface model meshes are matched. Cerebral cortex matching problems can thus benefit from the tremendous speed advantage of spectral methods, which are able to calculate a cortex matching in seconds rather than hours. Moreover, spectral methods are extended in order to use additional information that can improve matching. Additional information, such as sulcal depth, surface curvature, and cortical thickness can be represented in a flexible way into graph node weights (rather than only into graph edge weights) and as extra embedded coordinates. In control experiments, cortex matching becomes almost perfect when using additional information. With real data from 12 subjects, the results of 288 correspondence maps are 88% equivalent to (and strongly correlated with) the correspondences computed with FreeSurfer, a leading computational tool used for cerebral cortex matching. Our fast and flexible spectral correspondence method could open new possibilities for brain studies that involve different types of information and that were previously limited by the computational burden.