Are you a connector, or just well-connected?

I am constantly meeting professionals who boast about their “network” or Rolodex, and promise that they can connect me to just about anyone. They say that if I look at their LinkedIn connections and see someone who could help me, they’ll “try” to make an introduction. The funny thing is that most of these so-called connectors have a list (huge ones, in some cases) of connections they barely know. It could be someone they met at a networking function for 30 seconds, or someone who found their...