Connectivity of Growing Random Networks

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Abstract
A solution for the time-dependent and the age-dependent connectivity distributions of a growing random network model is presented. In the model, sites are added at constant rate and a link to an earlier site is made with a probability proportional to k^gamma, where k is the number of pre-existing connections to that site. The number of sites with k links is proportional to k^{-gamma}exp[-ak^{1-gamma}] for 0<=gamma1, one site connects to nearly all other sites, while the connectivities between the remaining sites undergo an infinite series of transitions as gamma varies between 1 and 2.

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