Ask HN: Restrict users to log in to my site with LinkedIn credentials only?

My website is targeted at MBA students (can't go into much detail beyond this - sorry!). It's very much in the prototype stage as of now.

I'm trying to reduce friction in the sign-up process as much as possible, and would like my users to register painlessly. Given that I'm focusing on a specific niche, would it be a good idea to limit registration through their LinkedIn credentials?

I'm wondering if I will limit my "market" as a result of doing this, and if I should also allow users to log in with the Google/Twitter/Facebook credentials as well.