Recommender systems (RSs) facilitate decision making by providing customised suggestions that are tailored to user preferences. Most existing RS methods focus on single-type behaviour modelling, such as ratings, whereas real-world user interactions are diverse, including activities such as view, add-to-cart and purchase. The main hypothesis in this thesis is that incorporating multi-type behavioural indicators enables the development of more comprehensive models that better reflect user preferences, enhancing recommendation performance. To capture heterogeneous user-item interactions more effectively, graph transformer (GT)-based RS methods have been adopted in the literature. These GT algorithms offer a hybrid framework that improves recommendation performance. However, most existing GNNbased approaches struggle with scalability in large-scale settings and have limited capability in modelling higher-order dependencies beyond pairwise user-item interactions. To address these limitations, hypergraph neural networks (HGNNs) have been proposed, which allow the representation of higher-order relationships involving multiple nodes. Despite their advantages in capturing intricate dependencies, HGNN-based methods remain computationally expensive, posing challenges in computational resource-constrained environments. In addition, applying model compression techniques to address this issue often leads to performance degradation. Motivated by these challenges, this research explores the question: Is it possible to reduce the computational cost of HGNN-based RS methods without compromising accuracy in large-scale settings? To address the limitations of existing methods, four novel approaches are proposed, based on: 1) lightweight hypergraph transformers, 2) hardware-algorithm co-design, 3) hyperbolic representation learning and 4) HGNN-enhanced Mixture-of-Agents (MoA) frameworks. The methods introduced in this research yield effective models that achieve improved performance while reducing memory usage and runtime, providing a foundation for more efficient and scalable RSs.