Is social network analysis a good product idea for a startup?

Well, I wouldn't say that "social network analysis is a good product idea", no. But I would say "social network analysis is an amazingly useful technology, and some novel application of it could be a great product". The hard part, as you've probably noticed, is figuring out how to apply the technology to solving an interesting problem, or enabling something cool and new that people will pay for (or focus enough eyeballs on, so you can make money on advertising).

I think one thing to do is just keep the tech itself in a sort of mental queue, and as you walk around, see stuff, read, encounter people, etc., just constantly ask yourself "how could SNA be useful to somebody in this situation?" And probably, eventually, you'll have an "aha" moment and realize "Shit, I could build this cool thing to do X!"

I would say, watch a lot, listen a lot, read a lot and think a lot. Ask questions, be curious and don't be afraid to daydream ridiculous ideas that you wind up discarding. But do carry around a notepad, or a smartphone/tablet with a notetaking app, or something so you can record your ideas when they come to you. Not much would be worse than having that great idea and then forgetting it before you write it down. Also, sometimes, a "not so great" idea that you go back and revisit, may turn into the seed for a better idea. So go back and re-read your old notes occasionally.

FWIW, we're working on using SNA as part of one of our products. Our idea (which is not completely novel anyway) is to apply SNA to enterprise search and use the network links to help rank results. There's more to our product than just that, but it is one element (to be fair, one we haven't really started implementing yet).