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 Erdős-Gallai theorem as a necessary condition on the graphicality of configuration model networks comprising clique subgraphs.
Citation
Mann , P S , Smith , V A , Mitchell , J B O , Jefferson , C A & Dobson , S A 2021 , ' Exact formula for bond percolation on cliques ' , Physical Review E - Statistical, Nonlinear, and Soft Matter Physics , vol. 104 , no. 2 , 024304 . https://doi.org/10.1103/PhysRevE.104.024304
Publication
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Status
Peer reviewed
ISSN
1539-3755Type
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.104.024304.
Description
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.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.