This study examined the behavior of a bullying epidemic on different social network structures using ideas from network theory, graph theory, and stochastic epidemic modeling. Three aspects of the bullying epidemic were investigated: the predictors for duration of the epidemic, the impact of different initial conditions on the epidemic, and the impact of different network structures on the epidemic. Overall, the more connected the network and the stronger the connection between each individual, the longer the bullying epidemic last. Introducing a more popular student as the first bully to the population would also lead to a longer duration for the bullying epidemic. These results suggest that teachers could educate students on the negative consequences of bullying, which could weaken the connections between susceptible students and the bully, and thus decrease the impact of the bullying epidemic in the classroom.