While I was having a discussion about my previous FriendFeed posts, I had mentioned that it would be interesting to see the split up of likes w.r.t the directed, shortest path distance. Following graph shows the number of likes that are received from people you directly subscribe to, or subscribe to 2 hops away, 3 hops away and so on...
Both from this graph and the earlier post, we can see that almost 45% of the likes are from people you directly subscribe to. But what is really interesting is that almost 90% of the remaining likes are accounted by friends who are just two or three steps away. FriendFeeders sure are a close bunch!
This type of locality of reference is also related to what sociologists have called the triangle closing. Partly, this is also due to the fact that FriendFeed tries to make it easier to attain "closing of triangles" by displaying the updates from friends who are just one step away. It would be worth looking into how this network's evolution takes place by recrawling FriendFeed subscription graph and observing how it changes. I suspect that through the likes and comments users find new friends and subscribe to their feeds: Your Friend's Friends who like you may be quite likable themselves!
I believe that models of Web graphs (small world, preferential attachment) are getting even more sophisticated in such social settings. The act of linking is not just creating a new hyperlink anymore -- but it is fragmented into actions such as "I subscribe to someone", "I comment on someones posts", "I like someones post". Such actions are not limited to FriendFeed alone. You can draw similar analogies in Youtube (watching, rating, commenting...), Flickr etc. As we explore these datasets through our empirical analysis, it might bring in a better understanding and intuition to build newer models for Social Graphs.
This data was generated using the 200,000 likes and the graph consisting of subscription information of over 75,000 users. The actual shortest path calculation was done using the Boost Graph Libraries (BGL). This is an amazing and extensive tool for graph analysis and quite frankly, I am a bit surprised that I hadn't used it before! I had used the MATLAB bridge but for very large graphs it is best to run the algorithms using BGL. But, more on that later!