A social network is a group of people, not larger than about 150 people, who help each other without making it conditional on the exact situation. This is not like a contact network, creative network or power network, which put very specific conditions on help.
The Simple English article on 'social network' has more detail.
Social network analysis
"The key notion from network analysis, that the interconnections between people can be used to understand and improve their interactions, has clear implications for CSCW research into communication systems, teamwork, and knowledge management." 
Key topics include:
Measurement - how are social networks being collected and measured?
Tools - what is the state-of-the-art for analyzing, visualizing and representing social networks?
Application - how are systems embedding social networks into the fabric of their design, and how can system designers distill the complexities of networks into user-oriented displays?
Evaluation - how does the use of social network systems change, facilitate, or hinder users and their collaborations?"
In general, social network analysis may play a formal role in determining what information affects the Consumerium buying signal and may also impact the way some aspects of power structure are interpreted.
See also the various social network services.