I've made a new friend who concerns me because she invites many of my friends out but doesn't include me. How would you treat this person.  ?

I'm a dude but I think I can help a little. First of all, don't jump to conclusions because there might be a perfectly valid reason why. This person might just be trying to connect with people one-on-one. I have a friend who invites me to everything, but never invites anyone else and it's just because he prefers to have one-on-one with me. He also hangs out with his other friends one-on-one, and he's a introvert like me so I actually am fine with just being around him. Now, I'm not saying that she isn't excluding you because that is also a good possibility. To be honest, just ask her why she doesn't invite you to things. Although don't say "why don't you invite me to anything", you might wanna ask something like "hey, so I've noticed you don't like hanging out with me much. Is there any problem?". If she pretends there is no problem that is a red flag, but remember if she is somebody who has a hard time admitting mistakes you might want to do this via text because it's easier for a lot of people to chat that way for whatever reason. Remember she is a new friend and you might not have quite gotten into the full loop, so give it some time because it might get better. The biggest red flag of all is if she says mean things about other people behind their backs, this is a HUGE sign of an unfaithful friend and you might want to pull yourself out of the loop if she's like that. Again, I'm a dude and you probably know that we handle things very differently (not necessarily in a better way). Try to ask yourself "what has she done to me?" and really think about it because it might be that you're a little annoyed that you don't get enough attention (I'm not saying that you seem like you're jealous, but you should always ask yourself that).

Never invite her to anything or anyone from that group; unless they change their tune. 

I wouldn't treat them in any way at all. They're not a friend.

Obviously you steer clear of her and not invite her out. She sounds like a narcissist.