Keeping the concept of "quality time" in mind, consider arriving a bit early or staying after the official end of networking events as a way to accelerate your relationship-building.
By arriving early I'm not talking about anything more than 10-15 minutes. There likely will be very few people there at that time, other than organizers, hosts, sponsors and perhaps service staff, but if you're one of the first to arrive you might get some focused time with folks who later on find themselves moving constantly through the crowd making sure everyone has what they need and the event is going smoothly.
If you arrive too early, say 30 minutes before the start, you could be a nuisance to the people trying to set everything up and make last minute fixes, but 10-15 minutes before the "official" start should be fine. If you don't know the organizers, hosts, and sponsors, this is a great time to meet them. If you make a good impression you may find that smooths your way to meeting other people.
If you arrive with a specific type of person you'd like to meet in mind and communicate that clearly and in a friendly manner to the people running the event, they'll be in a better place to make what may be a vital introduction.
Staying late is a good idea only if it seems natural and don't be the only guest who lingers - that might irritate polite hosts who really just want to call it a day. If it does work to stick around, volunteer to help clean up or straighten out if it seems appropriate. You also may find yourself involved in conversations that last beyond the posted end time - again, stay aware of the needs of the event organizers and if you and another guest are still gabbing away, consider taking it some place else.
At the opposite end of the spectrum is the "arrive late, leave early" approach, which seems to defeat the purpose of even showing up. I mean, why waste a clean shirt or blouse if you are just going to breeze through - that doesn't make much of an impression (at least not a positive one).
This post is one in a series on how to make the most of in-person networking events. If you're going to go (and I suggest you do if your business benefits from relationships), you might as have the most fun possible and give and receive the greatest benefits from the occasion.
If you know of a networking event in the greater Wilmington Area [which means to me anywhere from Topsail Island, NC to North Myrtle Beach, SC] that's open to visitors, drop me a note ahead of time and I'll try to post it.