In order to understand the organization of the cerebral cortex, it is necessary to create a map or parcellation of cortical areas. Reconstructions of the cortical surface created from structural MRI scans, are frequently used in neuroimaging as a common coordinate space for representing multimodal neuroimaging data. These meshes are used to investigate healthy brain organization as well as abnormalities in neurological and psychiatric conditions. We frame cerebral cortex parcellation as a mesh segmentation task, and address it by taking advantage of recent advances in generalizing convolutions to the graph domain. In particular, we propose to assess graph convolutional networks and graph attention networks, which, in contrast to previous mesh parcellation models, exploit the underlying structure of the data to make predictions. We show experimentally on the Human Connectome Project dataset that the proposed graph convolutional models outperform current state-of-the-art and baselines, highlighting the potential and applicability of these methods to tackle neuroimaging challenges, paving the road towards a better characterization of brain diseases.