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The Social Graph API makes information about the public connections between people on the Web easily available and useful for developers. Developers can query this public information to offer their users dramatically streamlined “add friends” functionality and other useful features.

Now here is what I understand of it -

We all know that Google crawls the web and figures out which pages link to each other. Google is also crawling the web to find out how sites are related to each other. This is done using -

a) “XFN”: You can change the links on your page (the <a href=”"> tags) to include a parameter called “rel”. “rel” basically indicates how is the linked site related to the current site - is it a friend’s site, or is it a colleague’s site, or is it another of my sites, etc.

b) “FOAF”: Include a series of tags at the top of your site page(s) to indicate who your friends are.

Google is basically going through the “rel” parameters and the FOAF xml tags and storing how one site is related to another. And they have now made this information available to everyone via their new API.

Take a look at the 3 minutes video here, particularly the scenario at the end.