to be Dunbarred (definition): to have so many people as friends/followers in a social network that one can no longer easily pay attention to new people. British anthropologist Robin Dunbar proposed that there is a limit to the number of people with whom one can maintain social relationships, and that the limit is a function of relative neocortex size; humans can maintain larger relationship networks than other primates, for example. See Wikipedia Dunbar Number. There are various hypotheses about what the limits might be and what they mean – the core idea is that we’re limited in the number of people we can connect with.
Update: the Urban Dictionary had a definition of to dunbaras a transitive verb, posted by judiec on Feb 4, 2010, meaning to unfriend someone because you already have too many friends.
To intentionally remove someone from your circle of friends by avoiding contact, hiding or in extreme measures moving away. This will normally be necessary due to dull behaviour, fun sapping or heightened arrogance.
So I submitted the intransitive definition, to be overloaded. Thanks, Audrey for the Urban Dictioary reference.