Percolation in random graphs with higher-order clustering
MetadataShow full item record
Altmetrics Handle Statistics
Altmetrics DOI Statistics
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.
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
Physical Review. E, Statistical, nonlinear, and soft matter physics
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.
DescriptionFunding: We acknowledge the School of Chemistry and the School of Biology of the University of St Andrews for the funding contributions for this work.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.