Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of minimum-weight cliques and other subgraphs in graphs
  with random edge weights   We determine, asymptotically in $n$, the distribution and mean of the weight
of a minimum-weight $k$-clique (or any strictly balanced graph $H$) in a
complete graph $K_n$ whose edge weights are independent random values drawn
from the uniform distribution or other continuous distributions. For the
clique, we also provide explicit (non-asymptotic) bounds on the distribution's
CDF in a form obtained directly from the Stein-Chen method, and in a looser but
simpler form. The direct form extends to other subgraphs and other edge-weight
distributions. We illustrate the clique results for various values of $k$ and
$n$. The results may be applied to evaluate whether an observed minimum-weight
copy of a graph $H$ in a network provides statistical evidence that the
network's edge weights are not independently distributed but have some
structure.

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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int