The social and economical impact a virus has in a population is not negligible. For this reason, gaining a theoretical understanding of the behavior of a virus is of prime importance. This project is going to be divided in several parts. First, we will discuss the topology of different graphs. Secondly, we are going to talk about the propagation of a virus on a graph, and the optimal nodes to do that. We will introduce the notion of cost function, and how relevant it is. Lastly, we will be talking about vaccinating a graph.