Networking

For those of you that landed a position/internship at a top firm, how much networking did you actually do?

Not to sound cocky, but after some extensive LinkedIn searching (stalking), I'm pretty confident that my resume is at least on par with the summer analysts that got positions at GS, MS, JPMC, etc. for this coming summer, so I feel like the only thing stopping me from landing an offer (apart from flunking a technical or something) would be me just not networking enough.

I've been reaching out to a ton of alumni and have been in contact with a few from several banks and hedge funds but I have no idea how much networking is really necessary to at least land an interview. Do I need to talk to 20+ people at each company? Is 3-5 enough? Trying to get a sense of whether I'm doing enough or if I really need to make networking like a part-time job this semester.