1. The process of selectively removing persons deemed offensive, disrespectful, or having questionable motives from one's social circle or collection of friends.
2. In social media, e.g. Facebook, MySpace, Google, Twitter, the process of deleting, removing or "unfriending" such persons from one's friends or contact list.
I'm about to perform a Facebook friendectomy because the things she keeps saying on my page are just plain stupid.