One of the most harmful consequences of social media is the rise of cyberbullying, which tends to be more sinister than traditional bullying, given that online records typically live on the Internet for quite a long time and are hard to control. In this article, we present a three-phase algorithm, called BullyNet, for detecting cyberbullies on Twitter social network. We exploit bullying tendencies by proposing a robust method for constructing a cyberbullying signed network (SN). We analyze tweets to determine their relation to cyberbullying while considering the context in which the tweets exist in order to optimize their bullying score. We also propose a centrality measure to detect cyberbullies from a cyberbullying SN and show that it outperforms other existing measures. We experiment on a data set of 5.6 million tweets, and our results show that the proposed approach can detect cyberbullies with high accuracy while being scalable with respect to the number of tweets.