References

1. Yu. A. Malkov, D. A. Yashunin. Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs. IEEE TPAMI, 2018. arXiv:1603.09320. — The HNSW paper.

2. Yu. Malkov, A. Ponomarenko, A. Logvinov, V. Krylov. Approximate nearest neighbor algorithm based on navigable small world graphs. Information Systems, 2014. — The flat NSW predecessor HNSW builds on.

3. William Pugh. Skip Lists: A Probabilistic Alternative to Balanced Trees. CACM, 1990. — The layered probabilistic structure HNSW borrows for its hierarchy.

4. Jon Kleinberg. Navigation in a small world. Nature, 2000. — Why greedy routing succeeds on the right graphs.

5. Y. Koren, R. Bell, C. Volinsky. Matrix Factorization Techniques for Recommender Systems. IEEE Computer, 2009. — The user/item embedding model behind the recommendation use case.

Related tools & systems

• FAISS (Meta) — IndexHNSWFlat and many other ANN indexes.
• hnswlib — the authors' compact C++/Python HNSW library.
• Apache Lucene / OpenSearch / Elasticsearch — native HNSW vector search.
• Vector databases — Qdrant, Weaviate, Milvus, Pinecone (HNSW-based indexes).

Related ideas

• MIPS (Maximum Inner Product Search) — the recommendation ranking problem; reduces to nearest-neighbor search via normalization or an extra coordinate.
• IVF-PQ / product quantization — memory-efficient ANN, often combined with graph indexes.

This book's code

• code/hnsw.py — the full from-scratch index.
• code/demo.py — recall vs. efficiency measurement.
• code/hnsw_search.py — the semantic-search CLI.

All depend only on NumPy and the standard library.