Connectivity of growing random networks

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites that link to earlier sites with a probability A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) similar to k(gamma), different behaviors arise for gamma < 1, <gamma> > 1, and gamma = 1. For gamma < 1, the number of shes with k links, Nk, varies as a stretched exponential. For <gamma> > 1, a single site connects to nearly all other sites. In the borderline case A(k) similar to k, the power law N-k similar to k(-nu) is found, where the exponent nu can be tuned to any value in the range 2 < <nu> < <infinity>.