Most of the models studied in evolutionary dynamics consider a well-mixed population. However, this is rarely the case in nature where geographical structure plays a role: migrations and local competition contribute to maintain genetic diversity in a structured population, resulting in a complex evolutionary dynamics. In order to take geographical structure into account, we study a model proposed by Lieberman et al. in which individuals are arranged on a graph. This model considers a weighted directed graph where one individual is placed at each node and replacement probabilities are defined on each edge; the size of the population is kept constant since a birth and a death event occur at each time step.