Scale free networks by preferential depletion

We show that not only preferential attachment but also preferential depletion leads to scale-free networks. In our model there is neither growth of new connections nor growth of new nodes. We start from a well connected network and implement a probabilistic purely depletion procedure. The resulting degree distribution exponent is typically less than two (5/3) as opposed to the case of the growth models studied before where the exponents are larger. We investigate the most important properties characterizing these networks, as the cluster size distribution, the average shortest path and the clustering coefficient.