* Social networks are tough, tough, tough. There are so many subtle UX issues (why did Facebook work but Friendster fail? Why did MySpace work for a while but ultimately fail?) and there's the ultimate chicken-and-egg problem. Do you really, truly understand why your idea will win?
* Do you think that you really need the YC Fellowship? Will that actually help you? What will you use the $ for?
As @patio11 tweeted the other night:
https://twitter.com/patio11/status/717474850927808512
"It has never in the history of mankind been cheaper to make software. You don't need funding you need a day job at McDonalds."
* I think your best bet - if you really believe in this idea - is to build a prototype on your own, show the world why you've built a better LinkedIn, and show us / investors / YC why your professional social network is better than LinkedIn, and back it up with hard growth numbers.
If this 'Apply HN' instead said something like:
"So we have an idea - it's LinkedIn without the spam. We built a prototype, and we've gotten 50,000 people in the < whatever > business community to use it. They love it. We're growing within this niche at 20% per week. But it's only two of us, and we need to grow. So here we are -- we'd love the YC Fellowship so we can put some real effort into X, then Y, and finally Z."
Do that, and you've got a winner.
My $0.02. Discount as you will, and best of luck to your team!