Abstract

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
Volume106
Issue number1
DOIs
Publication statusPublished - 20 Jul 2022

Keywords

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

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