A social network service focuses on building online communities of people who share interests and activities, or who are interested in exploring the interests and activities of others. Most social network software services are web based and provide a variety of ways for users to interact, such as e-mail and instant messaging services.

YouTube, MySpace, Odeo, Flickr, Match and Facebook – all in one solution named ‘Dolphin smart community builder’. Developed for creating dating sites, social networks, content sharing portals.
Dolphin is absolutely free.

Dolphin is based on: PHP, MySQL, Ajax, JavaScript, Flash, Java.
Official site: http://www.boonex.com/products/dolphin/. Demo site: http://www.boonex.com/products/dolphin/doldemo/
Dolphin software contains most popular features peculiar to a common social network. Among them:

• Blog
• User profile
• Forum
• Audio/Video sharing
• Friends invitation
• Private messaging
• User groups
• Voting
• And much more

This solution is optimal for rapid start of your own social network (of course, if your goal is to get free solution).
There are many analogous solutions:

• Pligg
• PHPIzabi
• Elgg
• PHPFox
• Other

Also there are services for creating social networks.
Among them:

• Ning
• Kickapps

This software does not provide the source code (are not open source), they provide API. All interaction is held using XML and JSON. Solutions are not free.