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 A(k) which depends on the number of preexisting links k to that site. For homogeneous connection kernels, A(k) approximately 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 a stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A(k) approximately k, the power law N(k) approximately k(-nu) is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity.

Keywords

ExponentPhysicsInfinityHomogeneousConnection (principal bundle)Gamma distributionCombinatoricsExponential functionPower lawRange (aeronautics)Distribution (mathematics)Statistical physicsMathematicsStatisticsMathematical analysisGeometryMaterials science

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Publication Info

Year
2000
Type
article
Volume
85
Issue
21
Pages
4629-4632
Citations
1177
Access
Closed

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P. L. Krapivsky, S. Redner, F. Leyvraz (2000). Connectivity of Growing Random Networks. Physical Review Letters , 85 (21) , 4629-4632. https://doi.org/10.1103/physrevlett.85.4629

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DOI
10.1103/physrevlett.85.4629