What does "connection" mean to you in this instance? That's the sticking point here. If a "connection" is simply "I can see a post written by that person every now and then" well, I'm gonna go ahead and say ridding yourself of that won't actually harm you socially. I absolutely question self-defined "relationships" that are held together by mass broadcasts of carefully crafted messages. For me, that's not a relationship. Granted, that's not a decision for me to make, but regardless. I fear we've all redefined what a "relationship" is without actually considering the ramifications.