This is the kind of thing you study in a branch of mathematics called Graph Theory. I know a bit about this because when I was an undergraduate, getting a degree in math, I studied this stuff. I proved theorums about how many edges you'd have to traverse to get from one point to another. There are many types of Graph Theory graphs, directed and undirected, for example. Some that you'd need two colors to paint, or three, but none need more than four (a theory that has been proven since I left school, thanks to computers).
Graphs are useful for modeling stuff that goes on in computers. They are also part of a field of math called combinatorics that's related to statistics, and also related to a highly theoretical area of math called topology.
Now if you showed that diagram to most educated people, they probably would call it a network, and before we talked about social graphs we called them social networks, and you know what -- they're exactly the same thing, and social network is a much less confusing term, so why don't we just stick with it? (Answer: we should, imho.) So if you don't want to sound like an idiot, call a social graph a social network and stand up for your right to understand technology, and make the techies actually do some useful stuff instead of making simple stuff sound complicated.
PS: This Google search illustrates. Most of the definitions of "graph" are what you'd expect if you weren't a math major.
PPS: Copy editors, just change "social graph" to "social network."
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