Connectivity of Growing Random Networks
Abstract
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of pre-existing links k to that site. For homogeneous connection kernels, A_k ~ k^gamma, different behaviors arise for gamma<1, gamma>1, and gamma=1. For gamma<1, the number of sites with k links, N_k, varies as stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A_k ~ k, the power law N_k ~k^{-nu} is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity.
Cite
@article{arxiv.cond-mat/0005139,
title = {Connectivity of Growing Random Networks},
author = {P. L. Krapivsky and S. Redner and F. Leyvraz},
journal= {arXiv preprint arXiv:cond-mat/0005139},
year = {2009}
}
Comments
4 pages, 2 figures, 2 column revtex format final version to appear in PRL; contains additional results