“Six Degrees of Separation” — John Guare’s play about a wealthy Manhattan couple whose lives are upended by a con artist claiming to be Sidney Poitier’s son — was the toast of the town when it had its premiere in 1990. A mere six months later, Frank Rich wrote in The New York Times that “its title has passed into the language.”

Image The playwright John Guare, backstage at the Vivian Beaumont Theater in 2010. Credit... Sara Krulwich/The New York Times

Mr. Guare did not invent the idea that everyone in the world is separated by only six other people, which emerged out of nearly a century of mathematical and psychological research. But it was the stickiness of his title — and the 1993 film version, starring Will Smith as the impostor — that blasted it “into the pop-culture stratosphere,” as the sociologist Duncan J. Watts put it in his book “Six Degrees: The Science of a Connected Age” (2003).

While the idea that we’re all connected may seem old hat in the age of the internet, fascination with it has yielded its own rich web of associations over the years. On the eve of the play’s first Broadway revival, which opens on Tuesday, April 25, here’s an unscientific look at a concept that links, among other things, the first issue of Psychology Today, the star of “Footloose” and a shirtless J. J. Abrams.