My freshman year of college, I had a roommate who participated in an internship program in Washington, D.C. At the end of the internship, the students in the program attended a networking event with alumni in the city. She told me that she and the other interns competed to collect business cards -- the “winner” was the one who ended the night with the most.
Hopefully, this isn’t the way you’re networking.
Of course, it’s important to close a conversation by getting the person's contact information, but treating networking with a “gotta catch ’em all” attitude is a mistake.
Networking isn’t about franticly gathering business cards and phone numbers as fast as you can and then hitting up your new “contacts” for favors. It’s about establishing mutually beneficial relationships -- and to do that, you have to do more than speed through a conversation.
Being strategic about the people you meet is more important than attempting to strike up a rapport with anybody who comes across your path. But don't limit yourself to only those people more senior than you -- meeting professionals at every level and across industries is critical to truly diversify your network.