In a social experiment that I was conducting, I was trying to count the number of people each user contacted in a period of 10 days. The population size was 100 for the experiment. Based on the values that I calculated, I fit a negative binomial distribution to the data (the Q-Q plot is given below).
Conventional wisdom says that most networks amongst humans follow a power law distribution. I am guessing that my population size is too small to make a full conclusion about anything but is there any kind of relation between a negative binomial distribution and a power law distribution? I am asking this because I read a few days back that Normal Distribution and Gamma distribution (whose discrete analogue is the negative binomial) have a special role in that many other distributions can be derived from the Gamma distribution. I am wondering if this is true even with the power law distribution. I am a beginner in statistics so kindly point me in the right direction if I am out of track.