A Simple Model of Scale-free Networks Driven by both Randomness and   Adaptability
  In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that it follows a power law with the degree exponent in the range of (2,infinity). We also find a way to derive an expression of the clustering coefficient for growing networks and compute the average path length through simulation. 
Dinghua Shi, Xiang Zhu, Liming Liu