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Average Jaccard index of random graphs
- Part of
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- Journal:
- Journal of Applied Probability / Volume 61 / Issue 4 / December 2024
- Published online by Cambridge University Press:
- 26 February 2024, pp. 1139-1152
- Print publication:
- December 2024
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- Article
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The asymptotic behavior of the Jaccard index in G(n, p), the classical Erdös–Rényi random graph model, is studied as n goes to infinity. We first derive the asymptotic distribution of the Jaccard index of any pair of distinct vertices, as well as the first two moments of this index. Then the average of the Jaccard indices over all vertex pairs in G(n, p) is shown to be asymptotically normal under an additional mild condition that
$np\to\infty$ and 
$n^2(1-p)\to\infty$.
