In this paper we examine the structure of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erds-Renyi and scale free random graphs. This model can be interpreted as a seasonal
n-strain model of disease spreading.
Original languageEnglish
Article number014304
Number of pages20
JournalPhysical Review. E, Statistical, nonlinear, and soft matter physics
Issue number1
Publication statusPublished - 20 Jul 2022


  • Complex networks
  • Epidemic spreading
  • Percolation
  • Co-infection


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