HNSW Explorer

How HNSW works

1. Layered graph: each node is randomly assigned a max layer using an exponential distribution. Most nodes only live at Layer 0; very few reach the top.
2. Within each layer: every node connects to its M nearest neighbors. Higher layers are sparse (few nodes, long edges = "highways"). Layer 0 is dense (all nodes, short edges = "local roads").
3. Search starts at the top: from a fixed entry point, greedily walk to the neighbor closest to the query, repeat until no improvement.
4. Drop down a layer and repeat: the position from the previous layer becomes the start of the next layer's walk. Each drop refines the result with finer-grained edges.
5. Layer 0 with ef: at the bottom layer, instead of stopping at the first local minimum, HNSW maintains a pool of ef best candidates and expands their neighborhoods. Larger ef → more accurate but slower.

Why it's fast: the top layers act like an index over the index — you cover huge distances in just a few hops, then zoom in. For N points, search visits roughly O(log N) nodes instead of N.