It's weird when I get random friend requests on Facebook. If I don't know you well...and/or haven't talked to you in person or via phone in the last year, I don't want you creeping on my photos. I just don't. My Facebook profile is presumed personal--because I don't have a professional presence there.
BTW: that pro presence on FB is called a page, not a profile, and if you're thinking of starting an author page do it here. No, you can't just convert your personal profile to a professional Facebook presence by cleaning up your act going forward. If people "friend" you it's personal. "Like" you, professional. But I digress.
I get all sorts of LinkedIn requests via email, which is even weirder to me than the rando FB requests. Because, as Dana Kaye so eloquently puts it, is primarily a B2B (business to business) network. So companies do their recruiting there, for instance. It can get you a job. But no one gets to know you there. Name me one person that even logs in to their LI account more than once a week (as opposed to several times a day to Twitter and FB). To quote Dana, "Skip LinkedIn and focus on the communities that matter."
Plus, requesting to be my contact on LI has the connotation that I'm somehow endorsing you to professionally. Which is weird to ask when I've never met you or read any of your work (even if I have, honestly). But, again, digressing.
In short, stoppit. I'm not connecting to you on Linked In.