Recent advancements in computer vision have highlighted the scalability of Vision Transformers (ViTs) across various tasks, yet challenges remain in balancing adaptability, computational efficiency, and the ability to model higher-order relationships. Vision Graph Neural Networks (ViGs) offer an alternative by leveraging graph-based methodologies but are hindered by the computational bottlenecks of clustering algorithms used for edge generation. To address these issues, we propose the Hypergraph Vision Transformer (HgVT), which incorporates a hierarchical bipartite hypergraph structure into the vision transformer framework to capture higher-order semantic relationships while maintaining computational efficiency. HgVT leverages population and diversity regularization for dynamic hypergraph construction without clustering, and expert edge pooling to enhance semantic extraction and facilitate graph-based image retrieval. Empirical results demonstrate that HgVT achieves state-of-the-art performance on image classification and competitive performance on image retrieval, positioning it as an efficient and adaptable framework for semantic-based vision tasks.