Structural parcellations are often built under the assumption of parcels' correspondences across patients. In the current work, we test the robustness of this hypothesis using graph matching strategies. Given a structural parcellation, we analyse a set of patients at different parcellation granularity (from 50 up to 1000 parcels). The aim of the analysis is to test via graph matching if the graphs obtained with a given parcellation should be considered as labelled or unlabelled. The results show a node correspondence for low resolution and the requirement of an unlabelled embedding for higher number of parcels. We showcase the graph matching results for the different parcellations as well as the importance of a correct geometrical embedding for unlabelled graphs to compute graph-valued statistics.