The six degrees of separation idea was not inspired by the website. Rather the other way around. Martin Gardner wrote about the idea in Scientific American before Kevin Bacon made any films, and long before the world wide web ever exists. Recent work on the problem suggests that populations (and electrical power grids, and various other things) aren't quite random graphs, nor are they regular graphs, but somewhere in between. Calling it small world theory, a publication in Nature last year suggested that these networks have this short step distance or handshake number because of the relatively few really long jumps. They still cluster, but the clusters have long-range connections. (e.g., you may know lots of people in your home town, but you also probably know someone who knows someone who works in your national legislature or congress; this would take you almost anywhere in your country in about four handshakes.)