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Scale-Free Networks are Ultrasmall

Reuven Cohen·Shlomo Havlin
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Abstract

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 2 3, 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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Reuven Cohen, Shlomo Havlin. 2003-02-05. Scale-Free Networks are Ultrasmall. https://doi.org/10.1103/physrevlett.90.058701

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