I think an interesting problem would be trying to deduce how likely you are likely to enjoy a piece of internet content by how well your friends like it. We all have different backgrounds and interest and some things have more mass appeal then others. If you take two friends, you can have widely different interest but the common interest between those to friends might be more likelihood to intersect your common interest. Now if something is liked amongst a wider variety of friends it could have a greater common interest but if something is liked a lot between just two friends then it might fit a more specific or niece common interest. There is potential here for both categorizing and rating information. For instance if I had five friends on my social network that liked math a lot then the fact that they all liked something could either mean it is a good piece of math content or it is something which has more mass appeal. It could even mean something which is mathematical but at a popular science level vs an academic level. It would be interesting to try and figure out how to use this information both to categorize and rate information for a user of a social network.