Presentation

We aim at familiarizing students with graphs, as well as the probabilistic tools that appear in their study

graphs are objects appearing in a number of domains of modern sciences. One can think of connected neurons in a brain, the network of interconnected webpages, dependence graphs of task in a complex project, or genealogical trees, tweet cascades, infection tree, etc.

The common characteristic of the above graphs is their size, which often make them impossible to treat in a deterministic fashion. We will see some probabilistic methods that can be used to obtain the properties of these graphs as well as different families of random graphs that allow modelization of these deterministic graphs.

We will study some interesting dynamics on those graphs, such as rumor propagation, opinion diffusion, contagion mechanism, etc.