Search systems often employ a re-ranking pipeline, wherein documents (or passages) from an initial pool of candidates are assigned new ranking scores. The process enables the use of highly-effective but expensive scoring functions that are not suitable for use directly in structures like inverted indices or approximate nearest neighbour indices. However, re-ranking pipelines are inherently limited by the recall of the initial candidate pool; documents that are not identified as candidates for re-ranking by the initial retrieval function cannot be identified. We propose a novel approach for overcoming the recall limitation based on the well-established clustering hypothesis. Throughout the re-ranking process, our approach adds documents to the pool that are most similar to the highest-scoring documents up to that point. This feedback process adapts the pool of candidates to those that may also yield high ranking scores, even if they were not present in the initial pool. It can also increase the score of documents that appear deeper in the pool that would have otherwise been skipped due to a limited re-ranking budget. We find that our Graph-based Adaptive Re-ranking (GAR) approach significantly improves the performance of re-ranking pipelines in terms of precision- and recall-oriented measures, is complementary to a variety of existing techniques (e.g., dense retrieval), is robust to its hyperparameters, and contributes minimally to computational and storage costs. For instance, on the MS MARCO passage ranking dataset, GAR can improve the nDCG of a BM25 candidate pool by up to 8% when applying a monoT5 ranker.