Notes : Social Networks : Models , Algorithms , and Applications

We specifically discussed the power law degree distribution which has degree distribution pk = C ·k−α where C is a constant and α > 1. While not all degree distributions will be power law, many of the degree distributions of observed networks will be heavy-tailed or long-tailed distributions. A heavy-tailed distribution is a distribution that is “heavier” than the exponential distribution. Here, “heavier” means that the tail is much longer than the exponential distribution (which drops off to zero rapidly). The exponential distribution takes the form f(x, λ) = λe−λx where λ is the rate parameter. Taking the log of the exponential distribution, we have log(f(x, λ)) = log(λ)− log(λx).