Exact formula for bond percolation on cliques

Peter Stephen Mann; V.A. Smith; John B. O. Mitchell; Christopher Anthony Jefferson; Simon Andrew Dobson

doi:10.1103/PhysRevE.104.024304

Exact formula for bond percolation on cliques

Peter Stephen Mann, V.A. Smith, John B. O. Mitchell, Christopher Anthony Jefferson, Simon Andrew Dobson

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Abstract

We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.

Original language	English
Article number	024304
Number of pages	10
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	104
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.104.024304
Publication status	Published - 4 Aug 2021

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Keywords

Complex networks
Bond percolation
Clustering

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10.1103/PhysRevE.104.024304

PhysRevE.104.024304
Copyright © 2021 American Physical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1103/PhysRevE.104.024304.
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https://arxiv.org/abs/2102.09261v1

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title = "Exact formula for bond percolation on cliques",

abstract = "We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erd{\H o}s-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.",

keywords = "Complex networks, Bond percolation, Clustering",

author = "Mann, \{Peter Stephen\} and V.A. Smith and Mitchell, \{John B. O.\} and Jefferson, \{Christopher Anthony\} and Dobson, \{Simon Andrew\}",

note = "The authors would like to thank the School of Computer Science, the School of Chemistry, and the School of Biology of the University of St Andrews for funding this work.",

year = "2021",

month = aug,

day = "4",

doi = "10.1103/PhysRevE.104.024304",

language = "English",

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journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",

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T1 - Exact formula for bond percolation on cliques

AU - Mann, Peter Stephen

AU - Smith, V.A.

AU - Mitchell, John B. O.

AU - Jefferson, Christopher Anthony

AU - Dobson, Simon Andrew

N1 - The authors would like to thank the School of Computer Science, the School of Chemistry, and the School of Biology of the University of St Andrews for funding this work.

PY - 2021/8/4

Y1 - 2021/8/4

N2 - We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.

AB - We present exact solutions for the size of the giant connected component of complex networks composed of cliques following bond percolation. We use our theoretical result to find the location of the percolation threshold of the model, providing analytical solutions where possible. We expect the results derived here to be useful to a wide variety of applications including graph theory, epidemiology, percolation, and lattice gas models, as well as fragmentation theory. We also examine the Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.

KW - Complex networks

KW - Bond percolation

KW - Clustering

UR - https://www.scopus.com/pages/publications/85112358408

U2 - 10.1103/PhysRevE.104.024304

DO - 10.1103/PhysRevE.104.024304

M3 - Article

SN - 1539-3755

VL - 104

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 2

M1 - 024304

ER -

Exact formula for bond percolation on cliques

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On the use of generating functions for topics in clustered networks

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Exact formula for bond percolation on cliques

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On the use of generating functions for topics in clustered networks

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