Here is a youth ministry community builder that will initially please your introverts but by the end will be a favorite of your extroverts.
Begin by making a series of different size loops out of rope, twine, clothesline -- whatever you have handy. Some loops should be small enough that, when laid on the floor or ground, only one person could stand inside of them. Others should be large enough to accommodate 3, 5, 10 people and so on. One rope loop should be big enough that, in some form or fashion, the entire group could be within its circumference, provided the group works together (e.g. some people on other people's backs, standing on each other's feet, holding someone off the ground, etc). Lay out all the loops in an open space.
Begin play by telling everyone that when you say "Go!" they must find a loop to stand within and noone's feet can be touching the ground outside a loop. Once everyone is in a loop, you call "Go!" again and everyone must move to a different loop. Meanwhile, your task is to covertly remove one of the loops. Repeat this tricky move after each round, leaving fewer and fewer loops for the group to use. Obviously, leave the largest loop for last, challenging the entire team to somehow get themselves inside the big loop at the same time. Be sure to provide spotters! You can find more community builder ideas here.