On connectivity and robustness of random graphs with inhomogeneity

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2022-09-05 DOI:10.1017/jpr.2022.32

Y. Shang

引用次数: 5

Abstract

Abstract The study of threshold functions has a long history in random graph theory. It is known that the thresholds for minimum degree k, k-connectivity, as well as k-robustness coincide for a binomial random graph. In this paper we consider an inhomogeneous random graph model, which is obtained by including each possible edge independently with an individual probability. Based on an intuitive concept of neighborhood density, we show two sufficient conditions guaranteeing k-connectivity and k-robustness, respectively, which are asymptotically equivalent. Our framework sheds some light on extending uniform threshold values in homogeneous random graphs to threshold landscapes in inhomogeneous random graphs.

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不均匀随机图的连通性和鲁棒性

摘要阈值函数的研究在随机图论中有着悠久的历史。已知最小度k、k连通性以及k鲁棒性的阈值对于二项式随机图是一致的。在本文中，我们考虑了一个非齐次随机图模型，它是通过以单个概率独立地包含每个可能的边而获得的。基于邻域密度的直观概念，我们分别给出了保证k-连通性和k-鲁棒性的两个充分条件，它们是渐近等价的。我们的框架为将齐次随机图中的一致阈值扩展到非齐次随机图中的阈值景观提供了一些启示。

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.