mySociety has some interesting maps that display the time it takes to travel from one part of the UK to another by public transport.
Instead of displaying how to get from A to B, the maps show where you can get to in a given period of time. Effectively, they show the real distance (in terms of time lost to the trip) between two points rather than the geographic distance.
I can see something like this for 'community distance' on the Web, where the realities of the social topography impact the ease with which two users find each other and then connect.
I may be the fabled 6 degrees away from George Bush but that's not to say our intermediaries would be willing to provide introductions (well at least most of my friends wouldn't broker trust for him, I can't speak for his friends doing the reverse).