The rapid growth of social media has been witnessed during recent years as a result of the prevalence of the internet. This trend brings an increasing interest in simulating social media which can provide valuable insights to both academic researchers and businesses. In this paper, we present a step-by-step approach of using Hawkes process, a self-activating stochastic process, to simulate Twitter activities and demonstrate how this model can be utilized to evaluate the chance of extremely rare web crises. Another goal of this research is to introduce a new strategy that implements Hawkes process on graph structures. Overall, we intend to extend the current Hawkes process to a wider range of scenarios and, in particular, create a more realistic simulation of Twitter activities by incorporating the actual user status and following-follower interactions between users.