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From Marketing Online

This excellent 70 word definition of social graph was devised by Jeremiah Owyang while he is was a social media analyst at Forrester.

"The Social Graph is the representation of our relationships. Today, these graphs define our personal, family, or business communities on social websites. Unfortunately, we’re duplicating our same Social Graph on multiple websites, resulting in inaccurate data and time spent managing it. Despite many challenges, our Social Graphs should be self-managed from a single trusted source, replicated to websites of our choosing, thus resulting in accurate, efficient, relationship management".