A social graph is a network of social profiles/identities and relationships between them, either on a single site like a silo, across the web, or in-person connections. The phrase was popularized by Google's now defunct Social Graph API.
A subset of the full social graph that only focuses on the relationships between different representations of the same single identity and ignores the social relations between multiple such identities. Makes the scope of crawling the entire graph much more manageable.
Google Social Graph API
The now defunct Social Graph API indexed XFN and FOAF data and provided a free and open REST API where people could query it. Also contained a Social Graph Node Mapper that created canonical identities for silo identities using the sgn:// protocol
See identengine. Focused on the identity graph subset of the social graph.
relspider – a project by Pelle Wessman that crawls identities using rel-me links. Focused on the identity graph subset of the social graph and to enable similar questions for that subset as the Google Social Graph once did. Started out as an experiment at Flattr to resolve verified ownership of web pages in an open, non-hands on way.
Facebook focuses heavily on their internal social graph, which eg. shines through in the name of their Graph API.