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

Petter Holme

Physica A: Statistical Mechanics and its Applications, 2007, vol. 377, issue 1, 315-322

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.

Keywords: Complex networks; Network analysis; Network dynamics; Scale-free networks (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:377:y:2007:i:1:p:315-322

DOI: 10.1016/j.physa.2006.11.024

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