When I make a new connection through LinkedIn I often go to see the shared connections which tells you a bit about the other person, and allows you to have conversation on how you both got to know a shared connection.
I decided to do the opposite and went to LinkedIn did a quick search of my well connected data center friends. I have 944 connections, and the three unnamed friends have more than than I have. Here is a surprise. For each of my three uber connected friends I have 191, 165, and 138 shared connections.
Metrics for a friendship may sound silly. You know who your good friends are.