Retrieval-Augmented Generation (RAG) has demonstrated significant potential in enhancing large language models (LLMs) by supplementing external knowledge. However, existing approaches focus primarily on retrieving isolated factual knowledge entities while neglecting the critical reasoning relationships. To address this limitation, Graph-Augmented Generation (GraphRAG) has emerged as an effective solution, which explicitly integrates structured knowledge graphs to support complex reasoning tasks. Although diverse graph construction methods have been explored, they typically rely on static, query-agnostic graphs constructed via fixed heuristics. We are thereby motivated to propose a query-centric retrieval framework that adaptively constructs a graph tailored to each query. However, it is challenging to accurately identify these latent relationships from queries to the corpus. Moreover, unifying multiple local-perspective connections into a globally coherent structured corpus introduces additional complexity. To this end, we introduce HyperRAG, a novel framework in the Hyperbolic space that captures both explicit entity-based links and implicit query-aware connections. Extensive experiments on three benchmark datasets demonstrate that HyperRAG consistently outperforms existing baselines.