Mathematics – Probability
Scientific paper
2008-10-17
Mathematics
Probability
12 pages
Scientific paper
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we propose a simple model of infection that enables to study the coincidence time of two random walkers on an arbitrary graph. By studying the coincidence time of a susceptible and an infected individual both moving in the graph we obtain estimates of the infection probability. The main result of this paper is to pinpoint the impact of the network topology on the infection probability. More precisely, we prove that for homogeneous graph including regular graphs and the classical Erdos-Renyi model, the coincidence time is inversely proportional to the number of nodes in the graph. We then study the model on power-law graphs, that exhibit heterogeneous connectivity patterns, and show the existence of a phase transition for the coincidence time depending on the parameter of the power-law of the degree distribution.
Draief Moez
Ganesh Arvind
No associations
LandOfFree
A model for infection on graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A model for infection on graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A model for infection on graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-352252