Millions of users follow each other on Twitter and form a large and complex network. The size of the network creates statistical and computational challenges on exploring and examining individual behavior on Twitter. Using a sample of 697,628 Korean Twitter users and 34 million relations, this study investigates the patterns of unfollow behavior on Twitter, i.e. people removing others from their Twitter follow lists. We use Exponential Random Graph Models (p*/ERGMs) and Statnet in R to examine the impacts of reciprocity, status, embeddedness, homophily, and informativeness on tie dissolution. We perform data processing, statistics calculation, network sampling, and Markov chain Monte Carlo (MCMC) simulation on Gordon, a unique supercomputer at the San Diego Supercomputer Center (SDSC). The process demonstrates the role of advanced computing technologies in social science studies.