The distance between galaxies (that aren't gravitationally bound to each other) increases over time.
Or should I first ask, is there a center?
Probably not. If you inflate a balloon, any point on its surface will move away from any other point on the surface. And yet, no surface point can claim to be central.
Note that in the balloon example, there is of course a central point within the volume of the balloon. This is where the analogy breaks down: In case of the universe, we do not assume the existence of an ambient higher-dimensional space.