The result is therefore quite boring. It's like saying famous actors have worked with other famous actors, and lots of actors can thereby trace their themselves through a chain of actors back to Charlie Chaplin. (Too bad it wasn't about genetics -- now that would have been interesting.)
The relationship between PhD student and advisor is often much more like apprentice and master than the relationship between two actors/actresses working together.
Indeed, perhaps a more apt analogy from acting would be the many famous actors who trained under Lee Strasberg (Al Pacino, Robert De Niro, Dustin Hoffman, Anne Bancroft, James Dean, Jane Fonda, Paul Newman, Ellen Burstyn and others).
Strasberg in turn was a student of the ideas of Konstantin Stanislavski[1].