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On connectivity and robustness of random graphs with inhomogeneity

Part of: Combinatorial probability Graph theory

Published online by Cambridge University Press:  05 September 2022

Yilun Shang Open the ORCID record for Yilun Shang [Opens in a new window]
Yilun Shang*
Affiliation:
Northumbria University
*
*Postal address: Department of Computer and Information Sciences, Northumbria University, NE1 8ST, Newcastle upon Tyne, UK. Email address: yilun.shang@northumbria.ac.uk
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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.

Keywords

Random graphconnectivityrobustnessthreshold

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 05C80: Random graphs 05C40: Connectivity
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 1 , March 2023 , pp. 284 - 294
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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