Spread of Infection over P.A. random graphs with edge insertion
Caio Alves, Rodrigo Ribeiro

TL;DR
This paper studies how infections spread rapidly in a special class of evolving random graphs that combine preferential attachment and edge insertion, showing that a small number of steps can infect a large portion of the network.
Contribution
It introduces a new model of random graphs with time-dependent edge insertion and proves rapid infection spread under certain conditions.
Findings
Infection spreads within 3 steps to a positive fraction of the graph.
Graphs are highly susceptible to infection under integrability conditions.
Provides a lower bound for maximum degree in the graph.
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.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Complex Network Analysis Techniques · Markov Chains and Monte Carlo Methods
