I think that the popularity of the phrase can be traced to a talk by Facebook's Mark Zuckerberg.
"Zuckerberg attributed the power of Facebook to the “social graph, ” the network of connections and relationships between people on the service. He said, “It’s the reason Facebook works.”Since then many authorities, bloggers, software houses and academics have all started to use the phrase. If I am honest in my reading I have found use of the phrase confusing. In my mind a graph is usually a visual representation of some mathematical data and a social graph is a representation of a social network; the sort of things student teachers were asked to provide on teaching practice to illustrate classroom relationships.
“Its changing the way the world works,” he said, pushing information out faster than any big company can. “As Facebook adds more and more people with more and more connections it continues growing and becomes more useful at a faster rate. We are going to use it spread information through the social graph.” The net effect of the social graph is that groups and application can achieve exponential growth, he said."
Why, then when we read about social networks (as might be found in Facebook, Ellg, Ning, Bebo et al) do we read of social graphs? It doesn't make sense.
What a joy it was to discover this evening that Dave Winer thinks the same as me!