Girl gives me strong eye contact as smile multiple times ?

Hey GC
here I was sitting in the outer area of my college which has benches , so I just sit beside a girl (just coincidentally) and she turns out to be quite pretty. There were these three occasions where both the our eyes were wandering and met(I felt she was trying to look out for opportunities to lock eyes with me) and she smiled, while maintaining eye contact.This happened 3 times . However 2 girls were sitting opposite of me, so I didn't open. I didn't want to make her feel awkward/make a fool of myself.After a while she just left with her book (I was assuming she'd stick around till the two girls opposite of her left if she was interested) and a bit later I find her sitting alone in the library.Was she smiling just to be polite or did I miss an opportunity ?

In a college setting, it is ok to introduce yourself to other students unless they are obviously engaged in their studies. If they are interested in you they will make time to talk to you privately. Think of college as one big social circle.

Now it could be she is naturally friendly and has a boyfriend, or is trying to recruit guys for her "Lifetime Virgin Prayer Circle" you won't know unless you introduce yourself, and get to know her. Too many guys think you have to pitch a date right away to every splittail with a pulse. Since it is social circle, there is value to everyone knowing who you are, and then dating who you want to ...

It depends. Generally in college you want to be more "friendly" and isolate later, and especially DO NOT get labeled as "that PUA guy."

In college, social circle game reigns supreme.

Quite a lot of effort required to smile at a guy right?

Be bright and well humored about it
"hey noticed you smiling, I am coming over because they say good emotions are contagious, true right?"
"so what you studying? im x btw"

First off, ignore the girls who are sitting opposite of you. Ofcourse they will observe you opening the other girl, but if you have good fundamentals they probably will get jealous. Also the girl who you would have opened would have noticed that I think, they usually do. You could have used a situational opener about something lame as the weather who cares. After a few minutes you would stop being strangers and the girls on the opposite of your bench would have stopped perceiving you as such. Maybe they would lament that no guy dares to talk to them in the college environment. In the end I think this is linked to frame control. By not daring to open the girl next to you, you have given the frame to the observing girls on the opposite side.

ALSO

Cockblocks directly or indirectly is a fact of life. I had instances where I isolated a girl but some guy tried to make us break circle, which I didn´t and the girl followed my lead. I can get rude to the point to tell someone to leave when I see that this happens.
I remember once a girl sending me strong interest cues, but 2 guys kept being try hard, trying to outdo me by verbal jousting. They were not aware of the girls interest, just more interested in being more `dominant`. But I wanted to keep my focus on the ball. I turned my back to those guys not even gracing them with a reply essentially freezing them out, I took the girl by her arm and isolated her. All this because I have prepared myself to do so.

You can try to wait for the most perfect moment, but trust and believe, even then some prick can appear like a wild pokemon out of the bushes and spoil your fun. You have to be prepared and trained in order to overcome this.