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 languageEnglish
Article number024304
Number of pages10
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number2
Publication statusPublished - 4 Aug 2021


  • Complex networks
  • Bond percolation
  • Clustering


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