They are not revolving around the 'centre of the universe'. They move outwards along helical(spring like)paths, the radius of the helix increasing as they move outwards. They are actually moving in absolute space, and the space is not expanding. It is this motion that causes the expansion of the universe. In this type of motion the distances between clusters are uniform (proportional to their masses), and so the universe is always 'uniform on a large scale'.