I think the idea of a single "centre of civilisation" is less than helpful. There were certainly a number of centre's of different civilisations, but if you try to plot the centre of these, there's a good chance you would end up in the middle of nowhere, or open ocean.
I think it's much more useful to think of a net with connections, with different levels of "zoom out".
For example, you could look at 0CE Rome, and get a good understanding of how the city ran. Zoom out to Italy, and have a good understanding of the 'Centre' of their empire. Zoom out to the entire empire, noticing a second clustering towards Egypt, and how trade flowed to the Parthian empire, into Germania and how there was even a trickle through the Sahara.
Then zoom out again to get an idea of how these all interacted with the other great empires in India and China. And how these were disconnected from the American empires at the time.
The course of the book is to focus on whatever team was winning at any given time, and how the actions of that winning team set up the game for the next winning team. As such, though... before the New World, northern/western Europe didn't have any winning teams, except for the Vikings (whose slave trade with Persia and the Arab world led to the formation of Russia as a nation and a power), and the brief victory of the Crusades. And China was never very ambitious beyond its own borders.
The book is also very focused on trade, not just war. And the brilliant goods of the East were the source of great trade.
Yes, but it's not exactly the same as the Western habit of maintaining colonies and puppet governments for a far-flung empire. China has done nothing analogous to, say, Britain's occupation of India.
What about Mediterranean bronze age though? There you have a trade based civilisation that AFAIK was far ahead of its Asian counterparts, possibly with the exception of the Indus Valley civilization. Also, I think that Rome was about on the same level as Han dynasty China, whether you look at trade, military, administration, technology etc. - it doesn't seem right to call one the center of civilization and the other a backwater.
I'm actually wanting to do a bit more investigation into the Bronze Age stuff. Long, long ago, I read Buckminster Fuller arguing that the Bronze Age could not have been centered in the Middle East (as we usually assume), because there's simply no significant tin deposits there. The only place in the world where copper and tin occur naturally together is in Thailand. And bronze is important because bronze fittings are essential for any seafaring ships larger/more complex than Polynesian pontoons. The only major tin deposits near Babylon are in the British Isles... and how do you get there?
I need to fact-check that, though. If Fuller is right, it really is a huge twist on the story of early global trade.
I think it's much more useful to think of a net with connections, with different levels of "zoom out".
For example, you could look at 0CE Rome, and get a good understanding of how the city ran. Zoom out to Italy, and have a good understanding of the 'Centre' of their empire. Zoom out to the entire empire, noticing a second clustering towards Egypt, and how trade flowed to the Parthian empire, into Germania and how there was even a trickle through the Sahara.
Then zoom out again to get an idea of how these all interacted with the other great empires in India and China. And how these were disconnected from the American empires at the time.