Most people's social graphs are too small (130 people) to be useful. Well we will use an extended social-graph, you might say, but if you are extending the social-graph, why not include the entire internet? Why would my social-graph contain better (more accurate and relevant) information about doing a thing than doathing.com?
The social-graph is a reduced set of the internet. It is probably easier to search, but how will the results be better than Google?
I think you are mistaking how to integrate the social graph into search. You don't do it by exclusively searching within the social graph, you use the social graph to augment your traditional search. The best way for me to show you what I mean is for you to look at the attempts blekko is making. Create an account, and connect your facebook profile, wait 1 hour, and then do searches with "/likes" appended. You'll still get mostly normal results but the instances where a friend has liked a site will be featured more prominently. Facebook has not been able to "just make a search engine" with the social graph because making a traditional search engine is a non-trivial challenge.
Hasn't google already taken a huge step towards this with their +1 initiative (which is obviously tied to G+)?
With Google's velocity, I think they're probably going to get to "social search" first (good luck to Blekko, but reliance on FB is not going to scale - especially when FB looks to monetize - social search is their meal ticket).
There's a lot of room between the average user's social graph and the entire internet. I think if you got the best 20% of the internet compiled intelligently based on your social graph, you'd be in good shape.
You have control of your own social graph, you don't have control over who puts a page up for Google to crawl. You're using the authority someone has as part of your network to filter what comes in to the network - search only on sites that friends-of-friends have recommended and you're unlikely to get spam or sites that are hard to navigate or that won't provide a good service. If I'm looking for new outdoor equipment I could look at the online stores that fellow scouts have used and recommended and so save time weeding out the better stores.
Just my immediate reaction to your question. There are clearly benefits in both types of search. Also this presupposes that FB aren't trying to inject advertised offerings in to your social-graph based search; probably a bad assumption as that there looks like gold to me.
The social-graph is a reduced set of the internet. It is probably easier to search, but how will the results be better than Google?