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

Abstract

Recently there have 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 en exotic and unintuitive 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 log log N (which we call a hypersmall-world regime). We characterize the degree-degree correlation and clustering properties of this class of networks.

arXiv commenterrors fixed, one new figure, to appear in Physica A

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Cited by in corpus (5)

• Critical phenomena in complex networks
• Onion structure and network robustness
• The effects of degree correlations on network topologies and robustness
• Transition from small to large world in growing networks
• Observability transitions in correlated networks