A population evolution model and its applications to random networks
  A general population evolution model is considered. Any individual of the population is characterized by its score. Certain general conditions are assumed concerning the number of the individuals and their scores. Asymptotic theorems are obtained for the number of individuals having some fixed score. It is proved that the score distribution is scale free. The result is applied to obtain the weight distributions of the cliques in a random graph evolution model. 
I. Fazekas, Cs. Nosz\'aly, A. Perecs\'enyi
math.PR