Howard's question..."Is your "public network" like a closet, a file cabinet, your high school yearbook, your business associates, your vendors, your clients, your personal contact database, or what?"
My answer...All of the above, plus.
Assuming you have some sort of logical (?) process by which you invite connections and by which you accept invitations, why would you want to risk bad feelings by cutting someone loose, just because the connection hasn't paid off in some substantial way?
One never knows what connection might develop into something more substantial than a place on a list.
Bad choices can be kicked off your list, with cause.
The list is effortless to keep.
It would be useful to have ways to sort our lists and to do mass (non-spam) messages based on our own criteria, just like in an email application.