This plot compiles data on empire sizes from AfroEurAsia, 3200BCE to present, ranked by size along the x axis in square 100kms (kilo-kilometers).

along the y axis, four variables are plotted

Size of the second largest empire in the same region (with moving average, square 100kms (kilo-kilometers squared), the regions being:

1. *Mesopotamia*, including the drainages of the Tigris and the Euphrates.
2. *Egypt*, the lower valley of the Nile.
3. *Europe*, including the Mediterranean and Aegean islands, that part of the Eurasian continent to the west of the Caucasus Mountains, but not Asia Minor (now Turkey);
4. *Africa;*
5. *West Asia* including Asia Minor, Mesopotamia, Syria, Persia, the Levant, and Bactria (Afghanistan).
6. *South Asia *including the Indus river valley;
7. *East Asia*, including China, Korea and Japan and Southeast Asia, but not Indonesia;

Largest city size in the empire (red, with exponential curve, x1000s of people)

Second largest city size in the empire (blue, with exponential curve, x1000s of people)

Ratio of first/second city size (linear plot, decreasing, fitting purple crosses)

The irregularities are of interest but not statistically significant:

below size 1500sqkk does the 2nd largest empire scale at 2/3rds the size of the first, but above that there are only three largest empires, so no firm conclusion can be drawn above that scale.

primate city outliers (over 2:1 larger than second city) are frequent in empires under size 1000sqkk

dropoff between size 1500 and size 2500sqkk in relative size of second largest empire (this suggests an absolute size range at which empires may become universal by defeating opponents) - but this is produced by only two largest empires, Muscovy-Russia-USSR (1720-1950), and Mongol-Yuan (1250-1290).

a lower primate city effect (purple line) tends to stabilize (at a 1.4:1 population ratio rather than 1.6:1) above empire size 1500; and there is a recovery above size 2500sqkk of relative size of second largest empire to constant size of 2000sqkk - but these are artifacts as these series pertain only to Britain, 1860-1920.

1750 empires are coded on the 1-4000sqkk scale, but there are only about 150 cases with data on first and second cities. The USSR is 2230sqkk; the largest empire, at 3550sqkk, is the British Empire in 1920, about 13.7 million square miles. Keep in mind, however, that if the second largest empire in the British Empire period is Russia there is another time period in which Russia is listed as a "largest" empire.