LinkdeIn today introduced "InMaps," an interactive visual representation of your professional universe that answers all of the above questions.
Here's how it works: your map is color-coded to represent different affiliations or groups from your professional career, such as your previous employer, college classmates, or industries you've worked in. In my InMap, my LinkedIn colleagues are blue, while my former colleagues at Yahoo Analytics are pink and other at Yahoo are green and my Carnegie Mellon classmates are orange and tangerine.
Bigger names represent people who are the most connected within that specific cluster or group. When you click on a contact within a circle you'll see their profile pop up on the right, as well as lines highlighting how they're connected to your connections.
More Info: InMaps