What do Small World Networks and Kevin Bacon have in Common?

In a strange case of seredipity, while I was reading Here Comes Everybody by Clay Shirky I saw a fascinating documentary that used the Six Degrees of Kevin Bacon game to explain Small World networks. Shirky devoted a chapter of his book to networks (particularly how network theory helps explain social networks). It fascinated me and prompted a post called Six Degrees Makes for a Small World on the RISG blog.