I've spent the past week going over the ideas in Chris Dixon's excellent post titled graphs and thought the ideas were powerful enough that they are worth reiterating. The thesis is simple, in recent years many have been focused on social graphs (i.e. graphs bidirectional or one-way “friend” relationships between users) but there are other ways in which users can be connected to each other besides whether they are friends or not. The key points from Chris’s post are excerpted below

Facebook’s social graph is symmetric (if I am friends with you then you are friends with me) but not transitive (I can be friends with you without being friends with your friend).  You could say friendship is probabilistically transitive in the sense that I am more likely to like someone who is a friend’s friend then I am a user chosen at random. This is basis of Facebook’s friend recommendations.

Twitter’s graph is probably best thought of as an interest graph. One of Twitter’s central innovations was to discard symmetry: you can follow someone without them following you. This allowed Twitter to evolve into an extremely useful publishing platform, replacing RSS for many people. The Twitter graph isn’t transitive but one of its most powerful uses is retweeting, which gives the Twitter graph what might be called curated transitivity.
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Over the next few years we’ll see the rising importance of other types of graphs. Some examples:

Taste: At Hunch we’ve created what we call the taste graph. We created this implicitly from questions answered by users and other data sources. Our thesis is that for many activities – for example deciding what movie to see or blouse to buy – it’s more useful to have the neighbors on your graph be people with similar tastes versus people who are your friends.

Financial Trust: Social payment startups like Square and Venmo are creating financial graphs – the nodes are people and institutions and the relations are financial trust. These graphs are useful for preventing fraud, streamlining transactions, and lowering the barrier to accepting non-cash payments.

Endorsement: An endorsement graph is one in which people endorse institutions, products, services or other people for a particular skill or activity. LinkedIn created a successful professional graph and a less successful endorsement graph.

Local: Location-based startups like Foursquare let users create social graphs (which might evolve into better social graphs than what Facebook has since users seem to be more selective friending people in local apps). But probably more interesting are the people and venue graphs created by the check-in patterns. These local graphs could be useful for, among other things, recommendations, coupons, and advertising.

One of the things that has been interesting to watch is how many services have tried to build this other sorts of relationship graphs on top of Facebook Connect. Quora has tried to build an endorsement graph from Facebook Connect as a basis while Yelp has tried to build a location graph using Facebook's Instant Personalization and Facebook Connect as the foundation. As more of these sorts of relationships graphs between people and other entities are created it is slowly becoming clear to me that there are many scenarios where Facebook’s graph is not the best starting point.

Take this screenshot of the Facebook Friend’s Activity plugin on Engadget as an example.

What this plugin does is show which of my Facebook friends (i.e. mostly family, coworkers and high school friends) have found interesting on Engadget. I couldn’t help but think back to what Chris Dixon mentioned about Twitter being an “interest graph”. I realized that this feature would actually be more useful if it showed me what Engadget articles people I follow on Twitter found interesting rather than what my Facebook friends did.

As the utility of the social graph grows beyond providing a stream of updates from people in that graph to being reused in other contexts, the lack of universal appeal in some of these relationships will grow more obvious. Using Twitter as an example, I suspect if asked to chose between a widget on TechCrunch that shows what articles are interesting among your Facebook friends versus who you follow on Twitter a non-trivial amount of people would pick the latter.

Similarly I wonder how soon till we start seeing some of the endorsement graphs being built on services like LinkedIn and Quora being leveraged in other places where you need to vet the opinions of strangers such as Amazon or even Monster.com.

There are times I’ve debated with others whether there will be one social graph to rule them all and whether that graph will Facebook’s. Now I ‘m convinced that although their graph is likely to be the largest and most generally applicable in the long term, there is a market for social graphs based on relationship types other than whether someone is a “friend” or not which can still significantly improve the user experience on the Web.

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