One solution.

There are lots of ways you could translate this - take your pick.

I think 'social graph' might be an instance of a foreigner misusing an English phrase, and I'd be tempted to leave it out. You could say something like:

A social network is essentially a digital footprint of our relationships with others as expressed on LinkedIn or Facebook.

"inscribe  

verb (used with object), -scribed, -scrib·ing.
1. to address or dedicate (a book, photograph, etc.) informally to a person, especially by writing a brief personal note in or on it.
2. to mark (a surface) with words, characters, etc., especially in a durable or conspicuous way.
3. to write, print, mark, or engrave (words, characters, etc.).
4. to enroll, as on an official list."

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Note added at 2 hrs (2011-10-24 17:58:06 GMT)
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Before the days of internet, but the same meaning:
"A copy below of the deeds of the divine Augustus, ... and of the money which he spent for the state and Roman people, INSCRIBED ON two bronze pillars, which are set up in Rome."
http://classics.mit.edu/Augustus/deeds.html

Another couple of suggestions.