My friend Jim and I are having an argument over networking? Jim says it's better to be an open networker on LinkedIn; I say it's better to follow LinkedIn's suggestion -- and only connect with people I know well. Which is the better strategy?
There's no right answer. It's up to your own level of comfort, and depends on what purpose you'd like to use your network for.
That said, my personal preference is to only connect with people who know you well. Why? If you get a job lead through a networking contact -- and they don't know you well...they cannot vouch for you.
It's not who you know that matters -- it is whether or not they are willing to speak up for you.
In my opinion, that's what matters most. "I recommend you for any job that you are qualified for," is a pretty weak reference. So Is "I don't know her."