Connectivity of Growing Random Networks

P. L. Krapivsky, S. Redner, and F. Leyvraz
Phys. Rev. Lett. 85, 4629 – Published 20 November 2000
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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 that link to earlier sites with a probability Ak which depends on the number of preexisting links k to that site. For homogeneous connection kernels, Akkγ, different behaviors arise for γ<1, γ>1, and γ=1. For γ<1, the number of sites with k links, Nk, varies as a stretched exponential. For γ>1, a single site connects to nearly all other sites. In the borderline case Akk, the power law Nkkν is found, where the exponent ν can be tuned to any value in the range 2<ν<.

  • Received 8 May 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.4629

©2000 American Physical Society

Authors & Affiliations

P. L. Krapivsky1,2, S. Redner1, and F. Leyvraz3

  • 1Center for BioDynamics, Center for Polymer Studies, and Department of Physics, Boston University, Boston, Massachusetts 02215
  • 2CNRS, IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier, 31062 Toulouse, France
  • 3Centro Internacional de Ciencias, Cuernavaca, Morelos, Mexico

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Vol. 85, Iss. 21 — 20 November 2000

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