Sysomos recently published a study demonstrating that 97% of Twitter users are "related" to one another through the Six Degrees principle.  This study suggests that the Twitter universe is slightly more connected to one another than the Facebook universe.  That said, "connected" is a loose term.  I would guess that we're not necessarily more meaningfully connected to more people on Twitter than Facebook but that we follow and friend for different reasons. 

To the average user this data should be amazing.  This should offer incredible utility!  I can in theory, access almost anyone on Twitter... if I could only figure out who I know that knows someone that knows someone that knows them.  

Most networks are looking to the social graph for ad targeting and semantic, smarter experiences.  This is a mistake.  Users want and should demand visibility into their social graph, at least into the third degree.  LinkedIn offers it.  Why can't Facebook?  Or Twitter?