The Fediverse is a set of open source social networking applications that can communicate with each other.

fediverse.party MIGHT gives an overview of the different social networking applications that can communicate with each other. Some of the applications:

Fediverse Server Implementations

diaspora and its GitHub account;
Friendica and its GitHub account;
GNU social and its source repository;
Hubzilla and its git repository;
Mastodon and its GitHub repository;
Misskey and its GitHub repository;
PeerTube and its GitHub repository;
Pixelfed and its GitHub account;
Pleroma and its git repository ;
Plume and its GitHub account;
pump.io and its GitHub account;
Socialhome and its main git repository;
Zap and its main git repository, MIT license, PHP;

Fediverse Communication Protocols

ActivityPub and its specification repository at GitHub;
diaspora;
OStatus;
Zot has a "protocol Community Group";

P2P Social Network Software that is NOT Connected to the Fediverse

Non-P2P Open Source Social Network Software that MIGHT be Upgraded to Connect to the Fediverse

minds.com GitHub account and supposedly the minds.com is based on the Elgg social networking engine .