Scaling Behaviour of Developing and Decaying Networks

Abstract

We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barabási and Albert in the particular case of growing networks. The networks considered here evolve according to the following rules: (i) Each instant a new site is added, the probability of its connection to old sites is proportional to their connectivities. (ii) In addition, (a) new links between some old sites appear with probability proportional to the product of their connectivities or (b) some links between old sites are removed with equal probability.