Year: 2022
Type: article
Abstract: In this paper we examine the emergent structures 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 a collaborative branching process, where percolation is performed on the giant connected component (GCC) instead. We investigate the behavior 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 Erdős-Renyi and scale-free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.
Source: Physical review. E
Institution: University of St Andrews
Language: Latvian
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4286209134