Spread of Infection over P.A. random graphs with edge insertion
Abstract
In this work we investigate a bootstrap percolation process on random graphs generated by a random graph model which combines preferential attachment and edge insertion between previously existing vertices. The probabilities of adding either a new vertex or a new connection between previously added vertices are time dependent and given by a function called the edge-step function. We show that under integrability conditions over the edge-step function the graphs are highly susceptible to the spread of infections, which requires only steps to infect a positive fraction of the whole graph. To prove this result, we rely on a quantitative lower bound for the maximum degree that might be of independent interest.
Cite
@article{arxiv.2103.16708,
title = {Spread of Infection over P.A. random graphs with edge insertion},
author = {Caio Alves and Rodrigo Ribeiro},
journal= {arXiv preprint arXiv:2103.16708},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1908.10260