First and second moments of the size distribution of bond percolation clusters on rings, paths and stars

Petar Jevtić; Nicolas Lanchier; Axel La Salle

doi:10.1016/j.spl.2020.108714

First and second moments of the size distribution of bond percolation clusters on rings, paths and stars

Petar Jevtić, Nicolas Lanchier, Axel La Salle

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The main objective of this paper is to study the first and second moments of the size of a typical cluster of bond percolation on ring, path, and star graphs. These graphs are essential building blocks of graphs that represent hybrid local area networks (LANs). In our setting, the edges are independently open with probability p, and the aim is to find the exact expressions for the first and second moments of the number of vertices in the cluster of open edges containing a vertex chosen uniformly at random. This work is motivated by a network science question of resilience as well as pricing of cyber risk in hybrid LANs.

Original language	English (US)
Article number	108714
Journal	Statistics and Probability Letters
Volume	161
DOIs	https://doi.org/10.1016/j.spl.2020.108714
State	Published - Jun 2020

Keywords

Bond percolation
Cluster size
Network resilience

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2020.108714

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title = "First and second moments of the size distribution of bond percolation clusters on rings, paths and stars",

abstract = "The main objective of this paper is to study the first and second moments of the size of a typical cluster of bond percolation on ring, path, and star graphs. These graphs are essential building blocks of graphs that represent hybrid local area networks (LANs). In our setting, the edges are independently open with probability p, and the aim is to find the exact expressions for the first and second moments of the number of vertices in the cluster of open edges containing a vertex chosen uniformly at random. This work is motivated by a network science question of resilience as well as pricing of cyber risk in hybrid LANs.",

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AU - Lanchier, Nicolas

AU - La Salle, Axel

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Y1 - 2020/6

N2 - The main objective of this paper is to study the first and second moments of the size of a typical cluster of bond percolation on ring, path, and star graphs. These graphs are essential building blocks of graphs that represent hybrid local area networks (LANs). In our setting, the edges are independently open with probability p, and the aim is to find the exact expressions for the first and second moments of the number of vertices in the cluster of open edges containing a vertex chosen uniformly at random. This work is motivated by a network science question of resilience as well as pricing of cyber risk in hybrid LANs.

AB - The main objective of this paper is to study the first and second moments of the size of a typical cluster of bond percolation on ring, path, and star graphs. These graphs are essential building blocks of graphs that represent hybrid local area networks (LANs). In our setting, the edges are independently open with probability p, and the aim is to find the exact expressions for the first and second moments of the number of vertices in the cluster of open edges containing a vertex chosen uniformly at random. This work is motivated by a network science question of resilience as well as pricing of cyber risk in hybrid LANs.

KW - Bond percolation

KW - Cluster size

KW - Network resilience

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JF - Statistics and Probability Letters

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ER -

First and second moments of the size distribution of bond percolation clusters on rings, paths and stars

Abstract

Keywords

ASJC Scopus subject areas

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