I don't believe that the citation list is copyrightable ("copyright does not protect facts" [1]). Ergo, anyone with access to a papers database could contribute, or you could port it over from other citation graphs.
Many papers databases will give you a formatted list of citations, which would be easier than trying to extract it from a set of arbitrarily formatted PDFs.
This is the really hard part that I am thinking on. I have not explore how could it be done yet. One spark idea is that each institution can build the graphs of their own separately and than they can be combined.
...but it's usually unusably slow. I'm curious: where would you get the data?