They began by using a computer to create lots of networks of virtual "friends", and measuring how many "handshakes" were needed to connect one friend to another in a totally different part of the network.

At one extreme were the utterly regular networks, where every friend only knows those right next to them. Devoid of any long range connections capable of linking, say, Bill Clinton to some store-keep in Hawaii, these networks typically demanded lots of handshakes before one person could be connected to another. Right at the other extreme were totally random networks, where people were just as likely to have personal friends in the White House as in Hawaiian stores.

Watts and Strogatz were intrigued by what happened between these two extremes, when the network was neither entirely regular nor utterly random. They expected the number of handshakes needed to link people to drop as the random links grew.

But what they discovered was startling: just a tiny number of random links was enough to "short-circuit" an otherwise huge, regular network, allowing apparently unrelated friends to be linked in just a few handshakes.

The computer revealed how easy it is to turn even a vast network into a small world: if only one in 100 people have a random link to anyone else in the network, the average number of handshakes drops ten-fold.

THEY ARE EVERYWHERE

But computer simulations are one thing; can small worlds be created so easily in the real one? Watts and Strogatz set about searching for a huge real-life network that they could probe for signs of the small world effect. They found the perfect, if unlikely, example in the Internet Movie Database, a computer searchable catalogue with the names of over 200,000 actors and the films they have appeared in.

Analyzing the database, Watts and Strogatz found that the typical actor has worked with around 60 others. If the showbiz network were completely regular, with no random short-circuits, that figure would imply that you'd typically have to go through 1,800 other actors and their films to link one actor to another. Yet the computer showed that it is possible to link any actor to any other via just three intermediaries. The vast movie Business is really a small world.

In fact, this had been known for years by movie buffs who play the so-called Kevin Bacon Game. The aim of the game is to link the eponymous American actor to any other via the fewest number of intermediaries.

Players were often struck by how often they could answer with the names of very few actors. For example, Bacon can be linked to Charlie Chaplin in just three steps: Bacon played in a film with Laurence Fishburn, who in turn was in a film with Marlon Brando, who himself once appeared with Chaplin.

Watts and Strogatz had confirmed what many players suspected was the explanation: the "short-circuiting" effect of a handful of actors whose careers span different eras, genres and cultures. For example, by starring in both Lethal Weapon and Hamlet, Mel Gibson short-circuits the all-action and classical genres, while martial arts actor Bruce Lee links the Chinese film industry to Hollywood.

The world of showbiz is now recognized as a classical small world. That is, it is made up of lots of little cliques of actors, most of whom stay in their own patch

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