Jeremiah Owyang - Web Strategist posted a really concise explanation of The Social Graph and why it matters, including how the implementation can be improved.

Executive Summary
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.
- Jeremiah Owyang

Read More Details at Explaining what the “Social Graph” is to your Executives

Definition: The Social Graph is the representation of our relationships. In present day context, these graphs define our personal, family, or business communities on social networking websites
- - Jeremiah Owyang