Lundi 2 avril 2012 à 14h, salle 55-65/211
Motivated by the analysis of social networks, we study a model of network that has both a given degree distribution and a tunable clustering coefficient. We analyze two types of epidemic processes on this random graph model: a diffusion process, which is characterized by an infection probability, each neighbor transmitting the epidemic independently, and a contagion model, which is inspired by a simple coordination game played on the network. Both types of processes have been used to model spread of new ideas, technologies, viruses or worms and results have been obtained for random graphs with no clustering. In this talk, we are interested in the impact of clustering on the growth processes. In both cases, we characterize conditions under which a global cascade is possible, and compute the cascade size explicitly, as a function of the degree distribution and the clustering coefficient. While clustering inhibits the diffusion process (in power-law and regular graphs), its impact for the contagion process is more subtle and depends on the connectivity of the graph: in a low connectivity regime, clustering also inhibits the contagion, while in a high connectivity regime, clustering favors the appearance of global cascades but reduces their size.