The structure of many real networks is not locally treelike and, hence, network analysis fails to characterize their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, arXiv:2006.06744], we developed analytical solutions to the percolation properties of random networks with homogeneous clustering (clusters whose nodes are degree equivalent). In this paper, we extend this model to investigate networks that contain clusters whose nodes are not degree equivalent, including multilayer networks. Through numerical examples, we show how this method can be used to investigate the properties of random complex networks with arbitrary clustering, extending the applicability of the configuration model and generating function formulation.
Original languageEnglish
Article number012309
Number of pages10
JournalPhysical Review. E, Statistical, nonlinear, and soft matter physics
Issue number1
Publication statusPublished - 22 Jan 2021


  • Complex networks
  • Random graphs
  • Clustered networks


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