Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Growth of Common Friends in a Preferential Attachment Model   The number of common friends (or connections) in a graph is a commonly used
measure of proximity between two nodes. Such measures are used in link
prediction algorithms and recommendation systems in large online social
networks. We obtain the rate of growth of the number of common friends in a
linear preferential attachment model. We apply our result to develop an
estimate for the number of common friends. We also observe a phase transition
in the limiting behavior of the number of common friends; depending on the
range of the parameters of the model, the growth is either power-law, or,
logarithmic, or static with the size of the graph.

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The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol