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Scale-free networks with a large- to hypersmall-world transition

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  • Holme, Petter

Abstract

Recently there has been a tremendous interest in models of networks with a power-law distribution of degree—so-called “scale-free networks.” It has been observed that such networks, normally, have extremely short path-lengths, scaling logarithmically or slower with system size. As an exotic and counterintuitive example we propose a simple stochastic model capable of generating scale-free networks with linearly scaling distances. Furthermore, by tuning a parameter the model undergoes a phase transition to a regime with extremely short average distances, apparently slower than loglogN (which we call a hypersmall-world regime). We characterize the degree–degree correlation and clustering properties of this class of networks.

Suggested Citation

  • Holme, Petter, 2007. "Scale-free networks with a large- to hypersmall-world transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 315-322.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:1:p:315-322
    DOI: 10.1016/j.physa.2006.11.024
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    1. B. J. Kim & A. Trusina & P. Minnhagen & K. Sneppen, 2005. "Self organized scale-free networks from merging and regeneration," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 43(3), pages 369-372, February.
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    3. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    4. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
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    Cited by:

    1. Liu, Ji & Deng, Guishi, 2009. "Link prediction in a user–object network based on time-weighted resource allocation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(17), pages 3643-3650.

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