Anyway, to take a stab at a difficulty relationship, i would say it is parabolic (quadratic), at least from the perfectionist standpoint, with the most difficult being around 2-3 cities since you no longer have the OCC special advantages, and yet don't have the power and flexability of larger civs.
From an expansionist/conqueror standpoint, i would venture that it is logarithmic, since it is very difficult to conquer with only 1 city, but there is a lot of diminishing returns for each new city after a while.
Of course since there are so many different ways to play and win the game, you really have to stick to a single approach, or your hardness graph will turn out to be rather flat (linear)

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April Cantor: Sire, in order to expand further we must first gain favor of the King
SCG: darn, I've never really got the hang of that tribute thing, guess it will be a long time until i make prince
*goes off and starts gifting gold and techs*
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