Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale-Free Networks are Ultrasmall   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<a<3
have a much smaller diameter, behaving as d ~ lnlnN. For a=3, our analysis
yields d ~ lnN/lnlnN, as obtained by Bollobas and Riordan, while for a>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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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph