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Facebook is kinda the only possible way of interaction.
Urm...why? adding her on facebook will seem weak and AFCish. Adding a girl on facebook should be last resort because its physically impossible for you to get in contact with her.
She lives next door to you. The best possible way of interaction is to walk over there, knock on her door and bossman it. I can guarantee that most guys that interact with her take the easy text/facebook approach.
You: Oh Hi there, I noticed you moved into the area. Thought I'd say hello.
Her: Oh hiiiii. blahblahblah
Get rapport make her laugh then hit her with
You: Hey I'm just off for a drink, you should join.
If she makes up/has an excuse then go for number close aka "Ah next time I'm free then, whats your number?"
if she's up for it, standard process. Take her out, have fun, escalate, go for k-close/f-close.
This not only increases your attraction no matter what as you don't bullshit around what you want but you can also gauge how cool she is about this kind of thing. Facebook will just show how dependent you are on non face2face communication. Plus if you add her and she accepts, she asks "Where do you live" and you say "right next to you" then she will just lower your value by saying something like "Why didn't you come say Hi?"