As I continue to work on my search engine, I've realized it's only part of the puzzle for internet exploration. The search engine could be the index for a specific internet browser made with the intent of browsing instead of searching.
I'm thinking this browser would have only one tab. It's your current location, and the rest is all about navigation. The history tree which shows you where you've been would also be very important. Easy access to all outgoing links from the page could also be interesting for navigation. Incoming links might add one more layer to the linking.
I think a button that takes users to a random page on the index would also be quite interesting.