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The distribution of minimum-weight cliques and other subgraphs in graphs with random edge weights

Frieze, Alan, Pegden, Wesley and Sorkin, Gregory B. (2018) The distribution of minimum-weight cliques and other subgraphs in graphs with random edge weights. SIAM Journal on Discrete Mathematics, 32 (3). pp. 2115-2133. ISSN 0895-4801

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Identification Number: 10.1137/17M1138303

Abstract

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 Kn 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.

Item Type: Article
Official URL: https://epubs.siam.org/journal/sjdmec
Additional Information: © 2018 SIAM
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 26 Apr 2018 11:34
Last Modified: 20 Feb 2019 06:46
URI: http://eprints.lse.ac.uk/id/eprint/87660

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