SpectRAG: Weighted Chunk Graphs for Token-Budgeted Context Selection in Multi-Hop Retrieval-Augmented Generation

Retrieval-augmented generation (RAG) systems ground large language models (LLMs) by retrieving external evidence and conditioning generation on the retrieved context. Although dense retrieval is effective for local semantic matching, independently ranked retrieval can return redundant passages, miss cross-chunk dependencies, and provide incomplete evidence for multi-hop reasoning. We propose SpectRAG, a spectral graph-augmented retrieval framework that combines hybrid candidate seeding, weighted chunk graph construction, graph-based expansion, spectral relevance propagation, and token-budgeted context selection. Document chunks are represented by dense semantic embeddings and graph-spectral coordinates derived from a weighted chunk graph whose edges encode semantic similarity, document adjacency, section hierarchy, shared entities, citation links, and similarity between LLM-generated utility questions. At query time, SpectRAG builds a high-recall seed set using exact inner-product search and hybrid relevance signals, expands it over the chunk graph, re-scores candidates using graph proximity and spectral information, and assembles the final context under a fixed token budget. The goal is not merely to retrieve individually similar chunks, but to construct a context that is relevant, diverse, structurally connected, and sufficient for grounded reasoning. Experiments on MultiHopRAG, UltraDomain, and long-document question-answering settings show that SpectRAG improves broad evidence recovery and achieves competitive generation quality against dense, hybrid, HyDE, LightRAG, and NaiveRAG baselines. The results further indicate that graph-spectral structure is particularly useful for inference-oriented and cross-document retrieval, while highlighting trade-offs in early precision, computational cost, and domain-dependent performance.