Twitter data have been used widely in times of pandemics and crises. Currently, the world is suffering from the outbreak of new coronavirus disease 2019 , in which the COVID-19 virus has infected more than one hundred and twenty million people worldwide with more than two million deaths. Consequently, people tend to share COVID-19-related content on social media extensively. As a new pandemic, only a small number of studies have been conducted to analyze COVID-19-related tweets, and even fewer were meant for Arabic tweets. This research explores the influence of the COVID-19 pandemic on Saudi users' tweeting behavior. In particular, the research adopts a social network analysis (SNA) for COVID-19 Arabic tweets. This approach is interesting, as it is based on analysis of social structures, such as Twitter users and the relationships among them, through the use of networks and graph theory without the contents of the tweets themselves. Based on 8905 collected Arabic tweets, this research resulted in three main contributions: 1) a visualization of the social network for COVID-19 tweets of Saudi users, 2) an identification of information sources that Twitter users employ during the COVID-19 pandemic, and 3) an identification of the most popular influencers among users of COVID-19 tweets. The results of this study may help identify the most popular Twitter influencers and those who deliver the information to Twitter users, utilizing them to increase awareness and deliver information and instructions to overcome the COVID-19 pandemic.