Connectivity of growing random networks

Citation
Pl. Krapivsky et al., Connectivity of growing random networks, PHYS REV L, 85(21), 2000, pp. 4629-4632
Citations number
23
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW LETTERS
ISSN journal
00319007 → ACNP
Volume
85
Issue
21
Year of publication
2000
Pages
4629 - 4632
Database
ISI
SICI code
0031-9007(20001120)85:21<4629:COGRN>2.0.ZU;2-I
Abstract
A solution for the time- and age-dependent connectivity distribution of a g rowing random network is presented. The network is built by adding sites th at link to earlier sites with a probability A(k) which depends on the numbe r 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, var ies 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>.