We show that not only preferential attachment but also preferential depletion
leads to scale-free networks. The resulting degree distribution exponents is
typically less than two (5/3) as opposed to the case of the growth models
studied before where the exponents are larger. Our approach applies in
particular to biological networks where in fact we find interesting agreement
with experimental measurements. We investigate the most important properties
characterizing these networks, as the cluster size distribution, the average
shortest path and the clustering coefficient.Comment: 8 pages, 4 figure