Six degrees of book similarities

The history of the idea of six degrees of separation has been written several times. For more information, works of Karinthy, Milgram, Barabási are good starters [link]. Erdös numbers, the Oracle of Bacon, the wikipedia game, etc. are well none elements of our popular culture.[link]

After frequent use of Amazon's 'customers who bought this book also bought...' service, the following idea quickly presents itself: Fetch the similarity graph of books from Amazon and make an 'Oracle of Bacon'-type service where links between any two books can be quickly found. How is Homer's Iliad related to Knuth's The Art of Computer Programming? Simple, those who bought the Iliad have also bought Plato's Republic, those who bought Plato's Republic also both Euclid's Elements, ... ... ...

Is the graph connected? If it is, what is its diameter, if not, what are the connected components. Which book is the most central? How does all this change if we limit ourselves to the few most important neighbors? Note that the items are not books in the everyday sense like 'Homer's Iliad' but products like 'The Iliad (Penguin Classics Deluxe Edition) (Paperback)'.

This could be an interesting tool for discovering new books, and it would be FUN.