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

Caio Alves; Rodrigo Ribeiro

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arXiv · 2103.16708

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

Caio Alves·Rodrigo Ribeiro

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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 $f$ 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 $3$ 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.

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BibTeX RIS

Caio Alves, Rodrigo Ribeiro. 2021-03-30. Spread of Infection over P.A. random graphs with edge insertion. https://arxiv.org/abs/2103.16708

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