As you are building your networks, be careful about LinkedIn's own narrow definition of colleague.
If you haven't worked for the same employer, the colleague invitation is a bad match for you. If your invitation is accepted, your new connection will face a screen asking for information about her "new position" at your company, as the narrow definition assumes your company corner offices shared a view.
This error style screen makes your new connection unsettled .... "did I screw up ... did he screw this thing up for me ..." and causes unnecessary confusion.
Using a shared group membership or a member's email address (first choose "other" in order to get to the email address prompt) is a better means of actually connecting on LinkedIn.