I don't really like "centre of the world" talk with historical civilizations. While China had influence on Europe (and vice versa), and was rich, for a long while, they didn't call the shots on a international matters in anywhere near the role the US does in global affairs. They think of themselves as having been the centre of the world like someone who studied only European history would think Europe was the centre of the world since ancient Egypt.
Of course, now they would be to a degree, if they fill the US's shoes. Lots of money flowing in and out of China all over the globe, their citizens posted all over, influence with the actions and laws of countries on the other side of the globe, etc. In the end, the historical norm is not important, I just don't like when people claim there was a centre of the world before we could quickly travel and communicate from one end to the other.
(I don't think they will have as much influence over global affairs as the US did since WW2. South America, India, other places have climbed out of the poverty hole enough to be a bit more self-deterministic.)