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Connectivity of Growing Random Networks

P. L. Krapivsky·S. Redner·F. Leyvraz
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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.

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BibTeXRIS

P. L. Krapivsky, S. Redner, F. Leyvraz. 2000-09-18. Connectivity of Growing Random Networks. https://doi.org/10.1103/physrevlett.85.4629

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