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Percolation in random graphs with higher-order clustering

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Mann_2021_Precolation_in_random_PhysRevE_103_012313.pdf (633.7Kb)
Date
25/01/2021
Author
Mann, Peter Stephen
Smith, V Anne
Mitchell, John B. O.
Dobson, Simon Andrew
Keywords
QA75 Electronic computers. Computer science
QD Chemistry
QH301 Biology
T-NDAS
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Abstract
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally treelike and does not contain short-range loops between neighbors. In this paper we use the generating function formulation to examine clustered networks that contain simple cycles and cliques of any order. We use the natural generalization to the Molloy-Reed criterion for these networks to describe their critical properties and derive an approximate analytical description of the size of the giant component, providing solutions for Poisson and power-law networks. We find that networks comprising larger simple cycles behave increasingly more treelike. Conversely, clustering composed of larger cliques increasingly deviate from the treelike solution, although the behavior is strongly dependent on the degree-assortativity.
Citation
Mann , P S , Smith , V A , Mitchell , J B O & Dobson , S A 2021 , ' Percolation in random graphs with higher-order clustering ' , Physical Review. E, Statistical, nonlinear, and soft matter physics , vol. 103 , no. 1 , 012313 . https://doi.org/10.1103/PhysRevE.103.012313
Publication
Physical Review. E, Statistical, nonlinear, and soft matter physics
Status
Peer reviewed
DOI
https://doi.org/10.1103/PhysRevE.103.012313
ISSN
1539-3755
Type
Journal article
Rights
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.103.012313.
Description
Funding: We acknowledge the School of Chemistry and the School of Biology of the University of St Andrews for the funding contributions for this work.
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  • University of St Andrews Research
URL
https://arxiv.org/abs/2006.06744
URI
http://hdl.handle.net/10023/21613

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