When Vector Similarity Fails: How Budget-Adaptive Graph Traversal Recovers Critical Documents That RAG Cannot Find

Retrieval-Augmented Generation (RAG) systems based on vector similarity consistently fail to retrieve documents that are semantically related to the answer but not directly similar to the query. This paper presents WordWeaveWeb, an open-source multi-tenant Graph-RAG platform, and introduces Auto-Hop, a budget-adaptive graph traversal algorithm that extends vector-based retrieval by following typed semantic relations between document chunks. Auto-Hop uses an inverted cosine similarity cost model (cost = 1 − similarity) with a finite traversal budget, producing adaptive exploration depth. Evaluated on two corpora (274 enterprise documents, 4 regulatory PDFs) across 8 questions, Graph-RAG with Auto-Hop improves context coverage by +100% to +180% and recovers critical documents unreachable by vector search at any threshold. Full codebase, corpora, and benchmark traces are released under MIT license.