English

Spread of Infection over P.A. random graphs with edge insertion

Probability 2021-04-01 v1

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 ff 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 33 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.

Keywords

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

R2 v1 2026-06-24T00:42:50.060Z