Average Jaccard index of random graphs

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2024-02-26 DOI:10.1017/jpr.2023.112

Qunqiang Feng, Shuai Guo, Zhishui Hu

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引用次数: 0

Abstract

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

$n^2(1-p)\to\infty$

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随机图的平均杰卡尔指数

本文研究了经典埃尔德斯-雷尼（Erdös-Rényi）随机图模型 G(n, p) 中 Jaccard 指数随 n 变为无穷大的渐近行为。我们首先推导出任意一对不同顶点的 Jaccard 指数的渐近分布，以及该指数的前两个矩。然后，在一个附加的温和条件下，即 $np\to\infty$ 和 $n^2(1-p)\to\infty$ ，G(n, p) 中所有顶点对的雅卡指数平均值被证明是渐近正态的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.