The authors propose HyperAdapter, a novel parameter-efficient fine-tuning method that adapts vision transformers in hyperedge space rather than token space. Existing adapter-based methods typically perform independent adaptations for each token, which overlooks structured relationships and can lead to redundant updates. HyperAdapter constructs a soft hypergraph over ViT tokens using prototype-based assignments to enable group-aware adaptation. The architecture aggregates token features into latent hyperedge representations and applies lightweight bottleneck adaptation at the hyperedge level. Updates are then diffused back to individual tokens via the hypergraph incidence structure, injecting an explicit structural inductive bias. Extensive experiments across diverse visual benchmarks demonstrate that this approach consistently outperforms strong PEFT baselines under comparable parameter budgets. The results highlight significant gains on tasks requiring structured reasoning and suggest that the choice of adaptation space is a critical dimension for efficient transfer.