Updated: Facebook has popularized the use of the term “social graph” as a way of describing all the various social connections you have to people in your life, both online and in the real world. But Chris Dixon, co-founder of Hunch.com and an angel investor in a number of web startups, says in a blog post published today that there is more than just one kind of social graph — in fact, he argues that there are actually about half a dozen different kinds, including graphs related to location and recommendations. Whether he is right or not, one thing seems pretty clear: Facebook not only wants to own them all, but is well on its way to doing so.

Dixon starts off with a little math, by noting that the term “graph” refers to a “set of nodes connected by edges.” The biggest online graph of all, he says, is the web itself, where individual webpages are nodes and the hyperlinks between them are the edges. In social graphs, “the nodes are people and the edges friendship,” or the relationships between those people. Dixon also describes how Facebook’s graph is symmetrical (meaning both sides of a connection must agree) and how Twitter’s is non-symmetrical (since you can follow anyone regardless of whether they follow you back).

Then comes what you might call a taxonomy of graphs, which Dixon says include:

  • Taste: This is the kind of graph that Hunch is trying to create, by looking at questions that users have answered about a variety of topics (the company also has a demo that reveals what it knows about you based on your tweets). GetGlue and other services are also explicitly going after this graph.
  • Financial Trust: Payment services such as Venmo and even Blippy (which lets you share your purchasing habits) are interested in this graph, which relates to financial connections between people and companies. PayPal and other payment companies are also obviously focused on this graph.
  • Endorsement: Dixon says that this graph involves people recommending things — or other people — and uses the example of LinkedIn, which is trying to create an endorsement graph for people who are looking for work. Facebook is also going after one aspect of this kind of graph with its “like” button plugins.
  • Local: Companies and services such as Foursquare, Gowalla and Loopt are obviously targeting this graph, which creates relationships between people and other people — as well as people and services — based on their physical location. As Dixon notes, this graph is highly appealing to advertisers.

Which brings me to the next thought that Dixon’s post triggered: namely, that Facebook has a massive head start on owning virtually every one of these sub-graphs, with the possible exception of the “financial trust” graph — and with Facebook Credits rolling out, it’s likely the giant social network will get its hooks into that one soon as well. Certainly recommendation-based graphs powered by the “likes” of 500 million users could be fairly powerful. And when it comes to local, Facebook appears to be working on features in that area as well, although it’s not clear what form they will take.

One other thing that struck me as I looked at the different categories of graph is that Google is virtually absent from this picture. It is a giant web entity with a multi-billion-dollar market cap, and hundreds of millions of people use and rely on it every day, but apart from flawed experiments such as Buzz and Wave, it has no place in those relationship graphs — which might explain reports of ongoing internal pressure at the web giant to come up with something like Google Me.

Update: As Mahendra Palsule (@ScepticGeek) has pointed out on Twitter in a response to this post, Google does have a number of social graph elements in its arsenal, including the Social Graph API, which is similar to Facebook’s open graph protocol. Google scans for relationships between users and pages that use standards such as XFN and FOAF, and connects those with Google Profiles, and then uses that information in its social search results. But I don’t think there’s any question that Google’s efforts have been substantially less successful than Facebook’s in terms of mass adoption.