How far apart are any two words?

People have six degrees of separation. Words, it turns out, have about the same. To measure it, we sampled a million random word pairs from the connected core of the Linguabase network and computed the shortest association chain between each pair — four days of processing on 32 cores. The mean came to 6.43 hops, shorter than we’d guessed and remarkably stable. 76% of pairs connect in seven hops or fewer.

Each hop follows a strong association — a crown’s gemstones lead to emerald’s foliage and on to a forest canopy; a flame becomes an ember, then a glowing memory, a mental recall, and finally the action to cancel. Every intermediate step makes sense on its own, which is what lets a person feel their way from one end to the other.

A bell curve centered on six

This is the “small world” structure familiar from social networks, and it was predicted: Ferrer i Cancho and Solé measured it in word co-occurrence networks in 2001, and Steyvers and Tenenbaum found it in thesaurus and word-association data in 2005. It persists at this scale — and it survives the deliberate down-ranking of generic superconnector words, so the short paths run through specific, meaningful associations.

Here are random examples at three distances. Two hops reads like a thesaurus entry; eight starts to feel like a relay race across the whole language. Inflected forms tend to produce the longest paths.

Double meanings don’t shorten the trip

You’d expect words with several meanings to act as wormholes. “Tear” touches both the eye and the rip; “head” is a body part, a leadership role, and a ship’s bow; “ground” reaches earth, coffee, and electrical circuits in a single step. Surely paths that route through such words come out shorter?

They don’t. Across 100,000 sampled paths containing a homograph, the average was 6.57 hops against the 6.43 baseline. Words with multiple meanings sit in densely connected neighborhoods whose regions were already close together, so what they contribute is choice: several creative routes covering the same distance.

The bridges that remain

Left to itself, shortest-path traffic piles up through generic hubs — words like “general” or “study” that connect to almost anything and tell you nothing. We penalized those superconnectors throughout the build. The interesting question is which words still emerge as natural bridges afterward.

The survivors earn their traffic honestly: “polish” bridges through homography (the verb and the nationality), “Renaissance” through historical reach, “jazz” by touching musical technique, cultural movements, and an era at once. On average these words sit about 2.2 hops from a path’s origin — the pivot where one domain hands off to another.

The words you can’t get to

Connectivity runs one way more often than you might expect. About 57% of the network’s terms appear among the top associations of at least one other word. The other 43% point outward but nothing points back: rare compounds (“stewing in one’s own grease”), deep technical vocabulary (“thermodispersion”), obscure proper nouns. From any common word you can reach nearly everything familiar; the long tail of English is a one-way door.

The playable band

The bell curve is also why hop navigation works as a game. For In Other Words, the daily puzzle this network was first built for, we tested puzzle distances and settled on three to seven hops — below three felt trivial, above seven players gave up. Nearly every pair of common words happens to land inside that band.

The game presents 17 association choices at each hop, which compounds to roughly 370 million distinct paths within seven hops of a typical starting word. Only a few hundred thousand of them reach the target — a random walker succeeds 0.05–0.27% of the time. Players do far better, because each step they choose means something.