I think you should try and guess the function, it will be in your first few guesses and that may help with getting the primary measure.
An obvious function with negative values?
- log -> already ruled out
- polynomial -> what would be the point?
- trigonometric -> what kind of country specific value would you put in a sin function?
- exponential -> positive for real values
So e^x, where x is the average number of friends (real + imaginary)?