The graph shows nothing about the population figure of said cities and Hackneyedscribe already covered it. We have no reliable estimates for Warring States urbanization simply because the sources and archaeology isn't sufficient, although its being speculated that urbanization did increase during the Han. However, there is absolutely no sufficient evidence to compare the urbanization ratio of the Persian Empire with contemporary China and hence its meaningless to make a comparison. In any case, the urbanization ratio of Italy alone in the Roman Empire was higher than medieval Europe, yet the population of Italy in 1300 CE is around 12.5 million while the population of Roman Italy in 1 CE is only around 8-9 million.It gives the density of urbanised settlements for given periods, speaking about territorial empires since 1000 BC. So yes, it is actually including the urbanisation rate of the Persian Empire (together with whatever other empire it may have been contemporary with). Look at the graphic again. The period of the late Warring States and the Qin dynasty actually sees a reduction in urbanisation, while it reaches a peak around the 6th and 5th centuries, the eras of Cyrus and Darius the Great. I was also comparing to Roman Europe since you're the one who made this comparison, but even then, most of the empire was in Europe, which had the destructive campaigns I mentioned, even in places like Greece where they destroyed Corinth in 146 BC and then further devastated it in the civil war between Pompey and Caesar, while the real major urban centres outside of Italy were in the east, mainly in Asia and Egypt, which arguably did have a greater population density than pre-Black Death late medieval Europe at least prior to the third century crisis. Even in North Africa, the Romans destroyed Carthage and the settlement they built over it was never big.
First, the population of Central and Inner Asia isn't in the census registration of 2 AD, which only covers the parts of the empire under direct bureaucratic control of the counties, so its irrelevant what it was. Second, the population of the Tarim Basin was very sparse, being estimated at around half a million by Cao Jinchun's "Demographic History of Different Provinces of China" in 2007. Details of provincial estimates are already made by numerous historians and Ge Jianxiong stated the maximum population capacity of northern China was around 50 million and that it remained the same from the Warring States down to the middle of the Ming, there is no need for you to do any guesstimates.Doesn't the Han also already include significant parts of Northern and Central Asia by this period? It was the time after they vassalised the Xiongnu after all and campaigned as far as the Greek kingdom of Da Yuan. Although those areas were certainly underpopulated compared to other parts of the empire, when adding to the 6-7 million it still should reach almost 10 million people, so the vicinity is more somewhere in the 50 million than 55, not far from the number I'm putting forward as the maximum for Warring States China, and which even if admitted as the number of only the seven warring states ignoring the rest of China, should produce an average of just over 7 million people, with the biggest states like Qin at its greatest extension prior to the unification of Qin Shi Huang getting over double that amount or about 15-16 million. But again, this should be seen as the maximum. One can reduce the number of the Han census by up to 20 million people (thus from 60 million to 40 million) assuming miscounting and lower number of people per households, meaning the area of the warring states could be as low as 30 million.
This implies that northern China during the Warring States could already have been 50 million and states such as Qin and Chu extended to large parts of southern China too, so the limit would be even beyond that. In any case 45 million is a rather conservative estimate on Ge Jianxiong's part based on his own methodologies, which leans toward the fact that the population of Warring States China wasn't too different from those under the Western Han at its height.
You seem to just arbitrarily draw upper limits with no proper methodology. There is no reason to believe that yes, even the entire Persian Empire can mobilize larger forces than the state of Qin, Chu, or even Zhao in the 3rd century BC. You have yet to prove, with scholarship using proper methodology that Persian urbanization rate is higher than these states or that its population is 50 million.I'm saying their numbers are somewhat exaggerated and that therefore at most they can only mobilise 200 thousand people when in duress, though I wasn't thinking of alliances when I said that. Like I keep saying, even universal conscription and Weberian central bureaucracy need population in order to mobilise greatly, and one needs to add resources as well. Centralised bureaucracies will not prevent economic collapse if they go around mobilising extreme numbers regularly, especially if they lose a battle. And again, I don't believe the Persian Empire could actually mobilise nearly half a million (not the full half a million, I meant something more in the order of 300 thousand men), I'm saying it's only more plausible given its territorial extension and high urbanisation, which leads credence to a population of nearly 50 million as a high end. I'm of the opinion that even with that high end, it wasn't capable of mobilising nearly half a million. Darius III only mobilised a force of about 200 thousand against Alexander when combining all the three great battles against him, and couldn't come to the relief of Tyre and Gaza either, though it's true all of this was after a period of internal chaos in the Persian Empire. Darius may well have mobilised up to double the amount had the Persian Empire been more stable.
The later figure is even more unlikely when you consider that even as late as 1900, the population of the region outside of Pakistan which constituted the entire Persian Empire was just over 50 million, even when places like Iran (where we have Islamic figures), Central Asia (Han records mentioning a population of only around 600,000 for Kangju), Afghanistan, and Egypt (where we have Roman era census showing only around 7 million people) clearly grew in size in the early modern period (broken down below):
Iran: 10 million
Iraq: 2 milion
Turkey: 12 million
Egypt: 10 million
Armenia: 1.3 million
Afghanistan: 3.6 million
Persian Central Asia: 7 million
To say that Achaemenid Persia in the 5th century BC already had a comparable population is suspicious especially without proper methodology.
The state of Qin, thanks to its universal conscription, should already be able to mobilize up to 1/15-1/10 of its population for war, as many later states with conscription and a centralized bureaucracy could do. This mean that with a population with some 5-10 million from the late 4th century onwards, the Qin would have no problem having half a million men on total reserve, and mobilize armies over half that size on short campaigns. Lets not forget that the Roman Republic in the early 2nd century BC was able to mobilize more forces and defeat the Seleucid Empire, even when the former only had a population size of around 8-9 million, having just Italy and a bit of Spain, whereas the Seleucid Empire under Antiochus almost re-established Alexander and Darius' empire, with the exception of Egypt, Greece and the extreme east. The Roman could proportionally mobilize larger amount of its forces than the Seleucid, and the Romans didn't even adopt universal conscription like the Qin.