What is HNSW and how does it work?

Hierarchical Navigable Small World, or HNSW, is a graph-based ANN algorithm that organizes vectors into a multi-layer graph where each layer contains a progressively smaller random subset of points. Search starts at the top layer with few nodes, greedily walks toward the query, and descends to denser layers, narrowing the search region at each step. The hierarchy gives logarithmic search time while the small-world connections ensure the greedy walk converges quickly. HNSW is the default index in Qdrant, Weaviate, Milvus, and pgvector.