<p>Graph neural networks (GNNs) have emerged as a prominent approach for capturing graph topology and modeling vertex-to-vertex relationships. They have been widely used in pattern recognition tasks including node and graph label prediction. However, when dealing with graphs from non-Euclidean domains, the relationships, and interdependencies between objects become more complex. Existing GNNs face limitations in handling a large number of model parameters in such complex graphs. To address this, we propose the integration of Geometric Algebra into graph neural networks, enabling the generalization of GNNs within the geometric space to learn geometric embeddings for nodes and graphs. Our proposed Graph Geometric Algebra Network (GGAN) enhances correlations among nodes by leveraging relations within the Geometric Algebra space. This approach reduces model complexity and improves the learning of graph representations. Through extensive experiments on various benchmark datasets, we demonstrate that our models, utilizing the properties of Geometric Algebra operations, outperform state-of-the-art methods in graph classification and semi-supervised node classification tasks. Our theoretical findings are empirically validated, confirming that our model achieves state-of-the-art performance.</p>