BuddyPress - WordPress social networking in a box.
Mastodon - Mastodon is a decentralized, open source social network. This is just one part of the network, run by the main developers of the project It is not focused on any particular niche interest - everyone is welcome!
Elgg - Opensource social network engine
Gab - Gab is an ad-free social network dedicated to free speech.
SocialEngine - Socialengine PHP: Elevating Your Online Community Experience.
Diaspora - The online social world where you are in control.