Graphs provide a powerful tool for coping with the non-uniformity and irregularity of 3D meshes, enabling multi-scale representations of 3D data. However, many existing methods either neglect the importance of relationships among elements within each region or fail to incorporate the hierarchical structure inherent in graph elements. This work introduces a novel representation that utilizes hierarchical segmentation techniques to address these limitations. Based on this hierarchical representation, two graph neural networks (GNNs) for 3D mesh classification are presented: (i) BM, a novel architecture that utilizes only the base graph; and (ii) HRGNet, a hierarchical model to explore multiple hierarchical levels. Experimental results demonstrate that the proposed models achieve high accuracy for the Manifold40 dataset, utilizing fewer parameters than other state-of-the-art methods. BM and HRGNet achieve results close to state-of-the-art, while BM has only 3% of the size of the best state-of-the-art method. HRGNet is 13% smaller than BM, thanks to the exploration of its hierarchical structure. For the SHREC2011 dataset, both proposed models still present high results (close to 90%) with only a small fraction of the state-of-the-art methods’ size (around 15%).