Please don't! This has been both tried before and it ended in a waste of resources, money (Diaspora, anyone?) and goodwill.
You can't beat the network effect of a social network with "we are open source", people don't care that much. You either have a usecase no one else has thought about, a technical killer feature or you don't try.
With a search engine, the network effect is not as big, but you better deliver something consistently better than Google right from the start.
Both are not fields ripe for disruption as the web browser game was in the mid-2000's.