Exact formula for bond percolation on cliques
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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.
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
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
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DescriptionThe 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.
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