Scale-Free Networks are Ultrasmall

Details Scale-Free Networks are Ultrasmall Scale-Free Networks are Ultrasmall

2002-05-23

arxiv.org/abs/cond-mat/0205476v2

Phys. Rev. Lett 90, 058701 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex, 4 pages, 2 eps figures, small corrections, added explanations

Scientific paper

10.1103/PhysRevLett.90.058701

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small world networks which is known to be d ~ lnN, we show, using analytical arguments, that scale free networks with 23, d ~ lnN. We also show that, for any a>2, one can construct a deterministic scale free network with d ~ lnlnN, and this construction yields the lowest possible diameter.

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